If A is an invertible matrix of order 3 and the determinant of A is 9, then the determinant of $A^{-1}$ is:

The number of all possible matrices of order $2 \times 2$ with each entry 0 or 1 having their determinants as positive value is :

If A and B are symmetric matrices of same order, then which of the following statements are true?

(A) $AB^T+B^TA$ is a skew-symmetric matrix.

(B) $AB^T-BA^T$ is a skew-symmetric matrix

(C) $(AB)^T(A^T)^{-1}=B$

(D) $(AB)^{-1}(BA)^T=A$

Choose the correct answer from the options given below:

If A is a 3-rowed square matrix and $|A| = 5$, then $|adjA|$ is equal to

If $\begin{vmatrix} 2x & 2 \\ 4 & x \end{vmatrix} = 10$, then $x$ is:

If A is a square matrix such that $A^2 = I$, then $(A+I)^3 + (A-I)^3 - 7A$ is equal to

For matrix $A = \begin{bmatrix} 2 & -3 \\ 3 & 4 \end{bmatrix}$ the value of $A^2 - 6A$ is equal to:(where I is an identity matrix of order 2)