If $A = \begin{bmatrix} 9 & 7 & 5 \\ 6 & 4 & 2 \\ 1 & 3 & 8 \end{bmatrix}$, then (cofactor of $a_{13}$ - cofactor of $a_{32}$ )will be equal to :

If $A = \begin{bmatrix} 3 & 2a \\ 1 & 5 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & 3 \\ b & 5 \end{bmatrix}$ both are singular matrices, then $a + b$ is equal to

The number of diagonal matrices of order 3 with elements either 1 or 2, is:

For a square matrix $A_{n \times n}$

(A) $|\operatorname{adj} \mathrm{A}|=|\mathrm{A}|^{\mathrm{n}-1}$

(B) $|\mathrm{A}|=|\operatorname{adj} \mathrm{A}|^{\mathrm{n}-1}$

(C) $\mathrm{A}(\operatorname{adj} \mathrm{A})=|\mathrm{A}|$

(D) $\left|\mathrm{A}^{-1}\right|=\frac{1}{|\mathrm{~A}|}$

If $A = \begin{bmatrix} 2 & 1 & -1 \\ 0 & 3 & -2 \\ k & 1 & 0 \end{bmatrix}$ is non-singular matrix, then the value(s) of $k$ belongs to:

[Where $R$ is the set of real numbers]

If $\begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix}$, where a, b and c are non zero constants, then the value of $\frac{1}{a} + \frac{1}{b} + \frac{1}{c}$ is

The matrix which is both symmetric and skew-symmetric, is a: