Matrices Properties - Discrete Mathematics Questions and Answers

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

Answer: a
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

Answer: a
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

Answer: c
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

Answer: c
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) Kⁿdet(B)
c) K³det(b)
d) None of the mentioned
View Answer

Answer: b
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).

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

Answer: a
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
View Answer

Answer: b
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
View Answer

Answer: b
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
View Answer

Answer: a
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
View Answer

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

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