# Discrete Mathematics Questions and Answers – Properties of Matrices

This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Properties of Matrices”.

1. The determinant of identity matrix is?
a) 1
b) 0
c) Depends on the matrix
d) None of the mentioned

Explanation: In identity matrix aii = 1, and all other elements = 0, hence the determinant is 1.

2. If determinant of a matrix A is Zero than __________
a) A is a Singular matrix
b) A is a non-Singular matrix
c) Can’t say
d) None of the mentioned

Explanation: Determinant of singular matrices are zero.

3. 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

Explanation: Determinant of a skew symmetric even ordered matrix A is a perfect square.

4. For a skew symmetric odd ordered matrix A of integers, which of the following will hold true?
a) det(A) = 9
b) det(A) = 81
c) det(A) = 0
d) det(A) = 4

Explanation: Determinant of a skew symmetric odd ordered matrix A is always 0.

5. Let A = [kaij]nxn, B = [aij]nxn, be an nxn matrices and k be a scalar then det(A) is equal to _________
a) Kdet(B)
b) Kndet(B)
c) K3det(b)
d) None of the mentioned

Explanation: The scalar is multiplied with each of the element of matrix A then determinant is multiplied, the number of row times to the scalar i.e. Kndet(B).
Note: Join free Sanfoundry classes at Telegram or Youtube

6. The Inverse exist only for non-singular matrices.
a) True
b) False

Explanation: Since for singular matrix det(A)=0.Hence Inverse does not exist.

7. If for a square matrix A and B, null matrix O, AB = O implies BA=O.
a) True
b) False

Explanation: Let A = [0 1 0 0], B = [1 0 0 0]AB=O and BA is not equal to O.

8. If for a square matrix A and B,null matrix O, AB = O implies A=O and B=O.
a) True
b) False

Explanation: Let A = [0 1 0 0], B = [1 0 0 0]AB=O and B, A is not equal to O.

9. Let A be a nilpotent matrix of order n then?
a) An = O
b) nA = O
c) A = nI, I is Identity matrix
d) None of the mentioned

Explanation: n is the smallest possible number such that An = O.

10. Which of the following property of matrix multiplication is correct?
a) Multiplication is not commutative in general
b) Multiplication is associative
c) Multiplication is distributive over addition
d) All of the mentioned

Explanation: Matrix multiplication is associative, distributive, but not commutative.

Sanfoundry Global Education & Learning Series – Discrete Mathematics.

To practice all areas of Discrete Mathematics, here is complete set of 1000+ Multiple Choice Questions and Answers.

If you find a mistake in question / option / answer, kindly take a screenshot and email to [email protected]