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 , AB^{T} is equal to

3. The matrix has det(A) = 100 and trace(A) = 14. The value of |a-b| is

- 4
- 3
- 2
- 1

4. Let M^{4} = I, (where I denotes the identity matrix) and M ≠ I, M^{2} ≠ I and M^{3} ≠ I. Then, for any natural number k, M^{-1} equals

- M
^{4k+1} - M
^{4k+2} - M
^{4k+3} - M
^{4k}

5. A real square matrix A is called skew-symmetric if

- A
^{T}= A - A
^{T}= A^{-1} - A
^{T}= -A - A
^{T}= A + A^{-1}

6. For , the determinant of A^{T}A^{-1} is

- sec
^{2}x - cos4x
- 1
- 0

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

- 1
- 2
- 0
- 5

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

- 48
- 25
- 14
- 0

10. The maximum value of the determinant among all 2 x 2 real symmetric matrices with trace 14 is

- 25
- 69
- 49
- 38

11. The determinant of matrix A is 5 and the determinant of matrix B is 40. The determinant of matrix AB is

- 200
- 100
- 150
- 75

12. Given that the determinant of the matrix is -12, the determinant of the matrix is

- -96
- -24
- 24
- 96

13. The determinant of matrix is

- 77
- 66
- 88
- 99

14. For matrices of same dimension M, N and scalar c, which one of these properties does not always hold?

- (M
^{T})^{T}= M - (cM)
^{T}= c(M)^{T} - (M+N)
^{T}= M^{T}+ N^{T} - 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}= P^{2}– 2PQ + Q^{2} - det(P+Q) = det(P) + det(Q)
- (P+Q)
^{2}= P^{2}+ PQ + PQ + Q^{2}