250+ TOP MCQs on Operations on Matrices and Answers

Discrete Mathematics online test on “Operations on Matrices”.

1. Let A and B be two matrices of same order, then state whether the given statement is true or false.

A + B = B + A

a) True
b) False

Answer: a
Clarification: Matrix addition is commutative.

2. Let A and B be two matrices of same order, then state whether the given statement is true or false.

AB = BA

a) True
b) False

Answer: b
Clarification: Matrix multiplication is not commutative.

3. Let A order(axb) and Border(cxd) be two matrices, then for AB to exist, correct relation is given by?
a) a = d
b) b = c
c) a = b
d) c = d

Answer: b
Clarification: Matrix multiplication exists only when column of first matrix is same as rows of second i.e b = c.

4. Let A order(axb) and Border(cxd) be two matrices, then if AB exists, the order of AB is?
a) axd
b) bxc
c) axb
d) cxd

Answer: a
Clarification: Matrix multiplication exists only when column of first matrix is same as rows of second i.e b = c also resultant matrix will have number of rows equal to first matrix and column equal to the second matrix.

5. Let A=[a_ij ] be an mxn matrix and k be a scalar then kA is equal to __________
a) [ka_ij ]_mxn
b) [a_ij/k ]_mxn
c) [k² a_ij]_mxn
d) None of the mentioned

Answer: a
Clarification: The scalar is multiplied with each of the element of matrix A.

6. The matrix multiplication is distrbutive over matrix addition.
a) True
b) False

Answer: a
Clarification: For matrix A, B, C, A(B+C) = AB + AC.

7. If for a square matrix A, A² = A then such a matrix is known as _________
a) Idempotent matrix
b) Orthagonal matrix
c) Null matrix
d) None of the mentioned

Answer: a
Clarification: A sqaure matrix is called an Idempotent matrix, if A² = A.

8. For matrix A, B.(A+B)^T = A^T + B^T and (AB)^T = A^TB^T if the orders of matrices are appropriate.
a) True
b) False

Answer: b
Clarification: (A+B)^T = A^T + B^T is correct but (AB)^T = B^TA^T(reversal law).

9. For matrix A, B if A – B = O, where O is a null matrix then?
a) A = O
b) B = O
c) A = B
d) None of the mentioned

Answer: c
Clarification: If subtraction of B from A results in the null matrix this means that A is equivalent to B.

10. All the diagonal elements of a skew-symmetric matrix is?
a) 0
b) 1
c) 2
d) Any integer

Answer: a
Clarification: Since for a skew symmetric matrix a_ij = -a_ij, this implies all diagonal elements should be zero.