Q.1
Correct Answer is:A,B,C
Solution Explain:
Q.2
Correct Answer is:A,B
Solution Explain:
Since, M2 = N4 ⇒ M2 – N4 = O ⇒ (M – N2)(M+N2) = O
[As M, N commute]
⇒ Det((M–N2)(M + N2)) = Det(O)
⇒ Det(M – N2). Det(M + N2) = 0
⇒ Det(M + N2) = 0
[As M ≠ N2 ⇒ M – N2 ≠ O ⇒ Det(M – N2) ≠ 0]
Also Det(M2 + MN2) = Det(M(M + N2)) = Det(M).Det(M + N2) = 0
⇒ There exist a non-zero matrix such that (M2 + MN2)U = O
Q.3
Correct Answer is:A,C,D
Solution Explain:
Q.4
Correct Answer is:A,C,D
Solution Explain:
Q.5
Correct Answer is:A,B,D
Solution Explain:
Q.6
Correct Answer is:C,D
Solution Explain:
Q.7
Correct Answer is:A,B
Solution Explain:
Q.8
Correct Answer is:A,B,C
Solution Explain:
Q.9
Correct Answer is:A,B
Solution Explain:
The transpose of a diagonal matrix is itself.
Also, the multiplication of A and D will be always commutative, where A and D are matrices of order 3 × 3 and D is diagonal matrix.
Q.10
Correct Answer is:B,C,D
Solution Explain:
Q.11
Correct Answer is:C,D
Solution Explain:
Q.12
Correct Answer is:B
Solution Explain:
Q.13
Correct Answer is:A,B,C,D
Solution Explain:
Q.14
Correct Answer is:A,B,C,D
Solution Explain:
Q.15
Correct Answer is:A,C,D
Solution Explain:
Q.16
Correct Answer is:B,C
Solution Explain:
Q.17
Correct Answer is:A,B,C
Solution Explain:
Q.18
Correct Answer is:A,B,C
Solution Explain:
