MCQ Questions Chapter 3 Matrices Class 12 Mathematics

Please refer to MCQ Questions Chapter 3 Matrices Class 12 Mathematics with answers provided below. These multiple-choice questions have been developed based on the latest NCERT book for class 12 Mathematics issued for the current academic year. We have provided MCQ Questions for Class 12 Mathematics for all chapters on our website. Students should learn the objective based questions for Chapter 3 Matrices in Class 12 Mathematics provided below to get more marks in exams.

Chapter 3 Matrices MCQ Questions

Question. If A= [aij] mxn and B= [bij]pxq and AB= BA then   
(a) n=p
(b) n=p, m=n
(c) m=n=p=q
(d) m=q

Question: If A and B are matrices of same order, then (AB’- BA’)  is a
(a) skew-symmetric matrix
(b) null matrix
(c) symmetric matrix
(d) unit matrix 

Question: If a, b and c are all different from zero such that 1/a +1/b +1/c=0,   then the matrix
(a) symmetric
(b) non-singular
(c) can be written as sum of a symmetric and a skew-symmetric matrix
(d) All of the above 

Question: For what value of x, the matrix

is singular
(a) x = 1, 2
(b) x = 0, 2
(c) x = 0, 1
(d) x = 0 ,3 

Question:

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

Question: For any 2x 2  matrix A, if A (a d j A) =

then |A | is equal to
(a) 0
(b) 10
(c) 20
(d) 100 

Question: The matrix A =

is
(a) unitary
(b) orthogonal
(c) nilpotent
(d) involutory

Question:

Question: If A is a singular matrix, then A adj (A )
(a) is a scalar matrix
(b) is a zero matrix
(c) is an identity matrix
(d) is an orthogonal matrix 

Question:

(a) A is singular
(b) | | A ¹ 0
(c) A is symmetric
(d) None of these

Question:

(a) A
(b)| A| 
(c) |A | I 
d) None of these

Question: Matrix A =

is invertible for
(a) k = 1
(b) k = – 1
(c) k = ± 1
(d) None of these

Question:

(a) A
(b) |A| 
(c) |A|I
(d) None of these

Question: If A is a skew-symmetric matrix of odd order, then A| is equal to
(a) 0
(b) n
(c) n²
(d) None of these

Question:

(a) 12⁴
(b) 13⁴
(c) 14⁴
(d) None of these

Question:

Question:

(a) 5
(b) 25
(c) –1
(d) 1

Question:

(a) 0
(b) – 1
(c) 1
(d) |A|

Question: If A²– A+I = 0, then the inverse of A is
a) A- I
(b) I- A
(c) A + 1
(d) A

Question:

(a) A
(b) A’
(c) 3A
(d) 3A

Question:

(a) – 1 6
(b) 1/ 3
(c) – 1/ 3
(d) 1/ 6

Question. If A is of order 2x³ and B is of order 3x², then the order of AB is :   
(a) 3x³
(b) 2x²
(c) 3x²
(d) 2x³

Question.  

(a) 5A
(b) 10A
(c) 16 A
(d) 32 A

Question.  

Question.

Question.  

(a) (3,7)
(b) (9,14)
(c) (5,14)
(d) (3,14)

Question.

(a) I 
(b) 2I
(c) 3I
(d) 4A

Question. If A is a square matrix , then AA^T + A^TA is :   
(a) Unit matrix
(b) null matrix
(c) symmetric matrix
(d) skew-symmetric matrix

Question. If a_ij= i + j then A = [𝑎_𝑖𝑗]3×4 is :   

Question.  

Question.

(a) (2,4), (4,2)
(b) (3,3),(3,4)
(c) (2,2),(1,1)
(d) none of above

Question.

(a) 1
(b) 2
(c) 1/2
(d) -2

Question.  

Question.  

(a) -5
(b) -1/5
(c) 1/25
(d) 25

Question.

(a) a = 2, b = -3
(b) a = -2, b = -3
(c) a = 1, b = 4
(d) none of above

Question.   

(a) 0
(b) I2
(c) -I2
(d) none of these

Question.

Question.

(d) none of above

Question.

(a) 1/3
(b) 5
(c) 3
(d) 1

Question.

Question.

(a) x = 3,y =1
(b) x = 2,y = 3
(c) x = 2,y = 4
(d) x = 3,y = 3

Question. Total number of possible matrices of order 3 x 3 with each entry 2 or 0 is
(a) 9
(b) 27
(c) 81
(d) 512

Question. If A and B are two matrices of the order 3 x m and 3 x n, respectively and m = n, then order of matrix (5A – 2B) is
(a)m x 3
(b) 3 x 3
(c)m x n
(d) 3 x n

Question.

(a) I
(b) 0
(c) 2I
(d) (1/2)I

Question.

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

Question.

(a) diagonal matrix
(b) symmetric matrix
(c) skew-symmetric matrix
(d) scalar matrix

Question. On using elementary row operation R₁ → R₁ – 3R₂ in the following

Question. 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. If A is matrix of order m x n and B is a matrix such that AB’ and B’A are both defined, then order of matrix B is
(a) m x m
(b) n x n
(c) n x m
(d) m x n

Question. If matrix A  =[ a_ij ]_2×2, where a_ij = 1, if i ≠ j = 0 and if i = j, then A² is equal to
(a) I
(b) A
(c) 0
(d) None of these

Question.

(a) identity matrix
(b) symmetric matrix
(c) skew-symmetric matrix
(d) None of these

Question. If A and B are matrices of same order, then (AB’ – BA’) is a
(a) skew-symmetric matrix
(b) null matrix
(c)symmetric matrix
(d) unit matrix

Question. On using elementary column operations C₂ → C₂ – 2C₁ in the

Question. For any two matrices A and B, we have
(a) AB = BA
(b) AB ≠ BA
(c) AB = O
(d) None of these

True/False

Question. Two matrices are equal, if they have same number of rows and same number of columns.

Question. Matrices of different order cannot be subtracted.

Question. A matrix denotes a number.

Question. Matrices of any order can be added.

Question. If matrix AB = 0, then A = 0 or B = 0 or both A and B are null matrices.

Question. Matrix multiplication is commutative.

Question. A square matrix where every element is unity is called an identity matrix.

Question. Matrix addition is associative as well as commutative.

Question. If A and B are two matrices of the same order, then A – B = B – A.

Question. If A and B are two square matrices of the same order, then A + B = B + A.

Question. If A, B and C are square matrices of same order, then AB = AC always implies that B = C.

Question. If each of the three matrices of the same order are symmetric, then their sum is a symmetric matrix.

Question. If A and B are any two matrices of the same order, then (AB)’ = A’B’.

Question. If A is skew-symmetric matrix, then A² is a symmetric matrix.

Question. Transpose of a column matrix is a column matrix.

Question. If A and B are two square matrices of the same order, then AB = BA.

Question. If (AB)’ = B’ A’, where A and B are not square matrices, then number of rows in A is equal to number of columns in B and number of columns in A is equal to number of rows in B.

Question. (AB)^-1 = A-1 · B^-1, where A and B are invertible matrices satisfying commutative property with respect to multiplication.

Question. AA’ is always a symmetric matrix for any matrix A.

Question.

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