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

View Answer

Explanation: In identity matrix a

_{ii}= 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

View Answer

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

View Answer

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

View Answer

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

5. Let A = [ka_{ij} ]_{nxn}, B = [a_{ij} ]_{nxn}, be an nxn matrices and k be a scalar then det(A) is equal to:

a) Kdet(B)

b) K^{n}det(B)

c) K^{3}det(b)

4) None of the mentioned

View Answer

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. K

^{n}det(B).

6. State True or False:

The Inverse exist only for non-singular matrices.

a) True

b) False

View Answer

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

7. State True or False:

If for a square matrix A and B,null matrix O, AB =O implies BA=O:

a) True

b) False

View Answer

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

8. State whether the given statement is True or False.

If for a square matrix A and B,null matrix O, AB =O implies A=O and B=O.

a) True

b) False

View Answer

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) A^{n} = O

b) nA = O

c) A = nI, I is Identity matrix

d) None of the mentioned

View Answer

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 genral

b) Multiplication is associative

c) Multiplication is distributive over addition

d) All of the mentioned

View Answer

Explantion: 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__.