Solve inverse of matrix MCQ, transpose of matrix MCQ, trace of matrix MCQ, types of matrix MCQ types questions with their answers.
1. The matrix P is the inverse of a matrix Q. If I denotes the identity matrix, which one of the following options is correct?
- PQ = I but QP ≠ I
- QP = I but PQ ≠ I
- PQ = I and QP = I
- PQ – QP = I
2. If , ABT is equal to
3. The matrix has det(A) = 100 and trace(A) = 14. The value of |a-b| is
4. Let M4 = I, (where I denotes the identity matrix) and M ≠ I, M2 ≠ I and M3 ≠ I. Then, for any natural number k, M-1 equals
5. A real square matrix A is called skew-symmetric if
- AT = A
- AT = A-1
- AT = -A
- AT = A + A-1
6. For , the determinant of ATA-1 is
7. Perform the following operations on the matrix
- Add the third row to the second row.
- Subtract the third column from the first column.
The determinant of the resultant matrix is
8. If any two columns of a determinant are interchanged, which one of the following statements regarding the value of the determinant is correct?
- absolute value remains unchanged but sign will change
- both absolute value and sign will change
- absolute value will change but sign will not change
- both absolute value and sign will remain unchanged
9. If the matrix A is such that then the determinant of A is equal to
10. The maximum value of the determinant among all 2 x 2 real symmetric matrices with trace 14 is
11. The determinant of matrix A is 5 and the determinant of matrix B is 40. The determinant of matrix AB is
12. Given that the determinant of the matrix is -12, the determinant of the matrix is
13. The determinant of matrix is
14. For matrices of same dimension M, N and scalar c, which one of these properties does not always hold?
- (MT)T = M
- (cM)T = c(M)T
- (M+N)T = MT + NT
- MN = NM
15. Which one of the following equations is a correct identity for arbitrary 3 x 3 real matrices P, Q and R?
- P(Q+R) = PQ + RP
- (P-Q)2 = P2 – 2PQ + Q2
- det(P+Q) = det(P) + det(Q)
- (P+Q)2 = P2 + PQ + PQ + Q2