**Matrices Class-12 MCQ** Type Questions for ISC Class-12 Maths. These MCQ / Objective Type Questions is based on latest reduced syllabus according 2021-22 session on bifurcated pattern. Main motto of MCQ Type Question is cracking the next upcoming exam of council. Visit official website CISCE for detail information about ISC Board Class-12 Maths.

** ISC Class-12 Maths Matrices Class-12 MCQ Type Questions **

Board | ISC |

Class | 12th (XII) |

Subject | Maths |

Ch-Name | Matrices |

Syllabus | on bifurcated syllabus (after reduction) |

Bifurcated pattern |
Semester-1 |

Session | 2021-22 |

Topic | MCQ / Objective Type Question |

** MCQ Type Questions for Class-12 of Matrices**

**Question 1: If a matrix A is both symmetric and skew symmetric then matrix A is**

(a) a scalar matrix

(b) a diagonal matrix

(c) a zero matrix of order n × n

(d) a rectangular matrix.

**Answer: (c) a zero matrix of order n × n**

**Question 2: If A = and A = A’ then**

**(a) x = 0, y = 5
(b) x = y
(c) x + y = 5
(d) x – y = 5**

**Answer: (b) x = y**

**Question 3: f A and B are symmetric matrices of the same order, then**

(a) AB is a symmetric matrix

(b) A – Bis askew-symmetric matrix

(c) AB + BA is a symmetric matrix

(d) AB – BA is a symmetric matrix

Answer: (c) AB + BA is a symmetric matrix

**Question 4: For any unit matrix I**

(a) I² = I

(b) |I| = 0

(c) |I| = 2

(d) |I| = 5

**Answer: (a) I² = I
**

**Question 5: A matrix A = [a _{ij}]_{m×n} is said to be symmetric if**

**(a) a _{ij} = 0
(b) a_{ij} = a_{ji}
(c) a_{ij} = a_{ij}
(d) a_{ij} = 1**

**Answer: (b) a _{ij} = a_{ji}**

**Question 6: A = [a _{ij}]_{m×n} is a square matrix if**

(a) m = n

(b) m < n

(c) m > n

(d) None of these

**Answer: (a) m = n
**

**Question 7: If A and B are square matrices then (AB)’ =**

(a) B’A’

(b) A’B’

(c) AB’

(d) A’B’

**Answer: (a) B’A’
**

**Question 8: The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is**

(a) 27

(b) 18

(c) 81

(d) 512.

**Answer: (d) 512.**

**Question 9: Assume X, Y, Z, W and P are matrices of order 2 × n, 3 × 1, 2 × p, n × 3 and p × k respectively. Now answer the following (4-5):**

The restrictions on n, k and p so that PY + WY will be defined are

(a) k = 3, p = n

(b) k is arbitrary, p = 2

(c) p is arbitrary

(d) k = 2,p = 3.

**Answer: (a) k = 3, p = n**

**Question 10: If n =p, then the order of the matrix 7X – 5Z is:**

** (**a) p × 2

(b) 2 × n

(c) n × 3

(d) p × n.

**Answer: (b) 2 × n
**

** Question 11: **For a skew symmetric even ordered matrix A of integers, which of the following will not hold true:

(a) det(A) = 9

(b) det(A) = 81

(c) det(A) = 7

(d) det(A) = 4

**Answer: (c) det(A) = 7**

** Question 12: **If A any square matrix then which of the following is not symmetric ?

(a) A−A^{t}

(b) A+A^{t}

(c) AA^{t}

(d) A^{t}A

**Answer: (a) A−A ^{t}**

** Question 13: **For what value of λ the following system of equations does not have a solution ? x + y + z = 6, 4x + λy – λz = 0, 3 x + 2y – 4 z = – 5

(a) 0

(b) 3

(c) -3

(d) 1

**Answer: (b) 3**

**Question 14: If a matrix has 6 elements, then number of possible orders of the matrix can be**

(a) 2

(b) 4

(c) 3

(d) 6

**Answer: (b) 4
**

**Question 15: Total number of possible matrices of order 2 × 3 with each entry 1 or 0 is**

(a) 6

(b) 36

(c) 32

(d) 64

**Answer: (d) 64**

**Question 16: If A is a square matrix such that A²=A, then (I + A)² – 3A is**

(a) I

(b) 2A

(c) 3I

(d) A

**Answer: (a) I
**

**Question 17: If A is a square matrix, then A – A’ is a**

(a) diagonal matrix

(b) skew-symmetric matrix

(c) symmetric matrix

(d) none of these

Answer: (b) skew-symmetric matrix

**Question 18: For any square matrix A, AA ^{T} is a**

(a) unit matrix

(b) symmetric matrix

(c) skew-symmetric matrix

(d) diagonal matrix

**Answer: (b) symmetric matrix**

**Question 19: If a matrix A is both symmetric and skew-symmetric, then**

(a) A is a diagonal matrix

(b) A is a zero matrix

(c) A is a scalar matrix

(d) A is a square matrix

Answer: (b) A is a zero matrix

**Question 20: If A ^{2} – A + I = O, then the inverse of A is**

(a) I – A

(b) A – I

(c) A

(d) A + I

**Answer: (a) I – A**

**Question 21: If A is a square matrix such that A ^{2} = I, then (A – I)^{3} + (A + I)^{3} – 7A is equal to**

(a) A

(b) I – A

(c) I + A

(d) 3A

Answer: (a) A

**Question 22: If A is an m × n matrix such that AB and BA are both defined, then B is a**

(a) m × n matrix

(b) n × m matrix

(c) n × n matrix

(d) m × n matrix

Answer: (b) n × m matrix

**Question 23: **

(a) A + B = B + A and A + (B + C) = (A + B) + C

(b) A + B = B + A and AC = BC

(c) A + B = B + A and AB = BC

(d) AC = BC and A = BC

Answer: (a) A + B = B + A and A + (B + C) = (A + B) + C

**Question 24: If , then A ^{2} – 5A is equal to**

(a) 2I

(b) 3I

(c) -2I

(d) null matrix

**Answer: (a) 2I**

**Question 25: The diagonal elements of a skew symmetric matrix are**

(a) all zeroes

(b) are all equal to some scalar k(≠ 0)

(c) can be any number

(d) none of these

**Answer: (a) all zeroes
**

**Question 26: If = 0, the value of x is**

(a) 3

(b) 8

(c) 24

(d) 0

**Answer: (b) 8
**

**Question 27: Let A be a non-singular matrix of the order 2 × 2 then |A ^{-1}|=**

(a) |A|

(b) 1/|A|

(c) 0

(d) 1

**Answer: (b) 1/|A|
**

**Question 28: If A = is a symmetric matrix, then x =**

(a) 4

(b) 3

(c) -4

(d) -3

Answer: (c) -4

**Question 29: **

(a) α = a^{2} + b^{2}, β = ab

(b) α = a^{2} + b^{2}, β = 2ab

(c) α = a^{2} + b^{2}, β = a^{2} – b^{2}

(d) α = 2ab, β = a^{2} + b^{2}

Answer: (b) α = a^{2} + b^{2}, β = 2ab

**Question 30: If a matrix is both symmetric matrix and skew symmetric matrix then**

(a) A is a diagonal matrix

(b) A is zero matrix

(c) A is scalar matrix

(d) None of these

**Answer: (b) A is zero matrix
**

**Question 31: If A, B are symmetric matrices of same order, then AB – BA is a**

(a) Skew-symmetric matrix

(b) Symmetric matrix

(c) Zero matrix

(d) Identity matrix.

**Answer: (a) Skew-symmetric matrix
**

**Question 32: Matrices A and B will be inverse of each other only if:**

(a) AB = BA

(b) AB – BA = O

(c) AB = O, BA = I

(d) AB = BA = I.

**Answer: (d) AB = BA = I.**

**Question 33: The number of 3 × 3 non-singular matrices, with four entries as 1 and all other entries as 0, is:**

(a) less than 4

(b) 5

(c) 6

(d) 7.

**Answer: (d) 7.**

** Question 34: **The system of equations, x + y + z = 1, 3 x + 6 y + z = 8, αx + 2 y + 3z = 1 has a unique solution for

(a) α not equal to 0

(b) all integral α

(c) all rational α

(d) all real α

**Answer: (b) all integral α**

** Question 35: **The inverse of a matrix is defined for

(a) Only square matrices

(b) Diagonal matrices

(c) all matrices

(d) Rectangular matrices

**Answer: (a) Only square matrices**

** Question 36: **The equations x + 2y + 2z = 1 and 2x + 4 y + 4z = 9 have

(a) infinitely many solutions.

(b) only one solution

(c) only two solutions

(d) no solution

**Answer: (d) no solution**

** Question 37: **square matrix A = [a

_{ij}]

_{n×n }is called a lower triangular matrix if aij = 0 for

(a) i is less than j

(b) i = j

(c) iis greater than j

(d) None of these

**Answer: (a) i is less than j**

** Question 38: **If the system of equationsx + 4 ay + az = 0, x + 3by + bz = 0 andx + 2 cy +cz = 0 have a non-zero solution,then a, b, c are in

(a) H.P.

(b) G.P.

(c) A.P.

(d) None of these

**Answer: (a) H.P.**

** Question 39: ** Rank of a non-zero matrix is always

(a) ⩾1

(b) 0

(c) greater than 1

(d) equal to 1

**Answer: (a) ⩾1**

**Question 40: The matrix P = is**

(a) square matrix

(b) diagonal matrix

(c) unit matrix

(d) None of these

**Answer: (a) square matrix
**

**Question 41: If the matrix A = is a symmetric matrix, then find the value of x, y and t respectively.**

(a) 4, 2, 3

(b) 4, 2, -3

(c) 4, 2, -7

(d) 2, 4, -7

Answer: (b) 4, 2, -3

**Question 42: If A = then A ^{4} – 2^{4 }(A – I) =**

(a) 5I + A

(b) 5I – A

(c) 5I

(d) 6I

Answer: (b) 5I – A

: End of **Matrices Class-12 MCQ** Type Questions for ISC Class-12 Maths :-

-: also visit :-

- ISC Class-12 Text book Solutions, Notes , Syllabus, Paper
- MCQ Type Questions ISC Class-12 Semester-1 Session 2021-22

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