# Matrices Class-12 MCQ Type Questions for ISC Class-12 Maths

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

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

Question 5: A matrix A = [aij]m×n is said to be symmetric if

(a) aij = 0
(b) aij = aji
(c) aij = aij
(d) aij = 1

Question 6: A = [aij]m×n is a square matrix if

(a) m = n
(b) m < n
(c) m > n
(d) None of these

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

(a) B’A’
(b) A’B’
(c) AB’
(d) A’B’

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.

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.

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

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

(a) A−At

(b) A+At

(c) AAt

(d) AtA

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

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

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

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

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

Question 18: For any square matrix A, AAT is a

(a) unit matrix
(b) symmetric matrix
(c) skew-symmetric matrix
(d) diagonal 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 A2 – A + I = O, then the inverse of A is

(a) I – A
(b) A – I
(c) A
(d) A + I

Question 21:  If A is a square matrix such that A2 = I, then (A – I)3 + (A + I)3 – 7A is equal to

(a) A
(b) I – A
(c) I + A
(d) 3A

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 A2 – 5A is equal to

(a) 2I
(b) 3I
(c) -2I
(d) null matrix

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

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

(a) 3
(b) 8
(c) 24
(d) 0

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

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

(a) 4
(b) 3
(c) -4
(d) -3

Question 29:

(a) α = a2 + b2, β = ab
(b) α = a2 + b2, β = 2ab
(c) α = a2 + b2, β = a2 – b2
(d) α = 2ab, β = a2 + b
2

Answer: (b) α = a2 + b2, 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.

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.

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

Question 35: The inverse of a matrix is defined for

(a) Only square matrices

(b) Diagonal matrices

(c) all matrices

(d) Rectangular 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

Question 37:  square matrix A = [aij]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

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

(a) ⩾1

(b) 0

(c) greater than 1

(d) equal to 1

Question 40:  The matrix P =  is

(a) square matrix
(b) diagonal matrix
(c) unit matrix
(d) None of these

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

Question 42:  If A =  then A4 – 2(A – I) =

(a) 5I + A
(b) 5I – A
(c) 5I
(d) 6I