If $A = \begin{bmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{bmatrix}$, then which of the following statements are TRUE?

[where $A_{ij}$ is the cofactor of the (i, j)th element, $a_{ij}$ of matrix A, $1 \gt i, j \le 3$.]

(A) $a_{11}A_{31} = -24$

(B) $a_{12}A_{32} = -66$

(C) $a_{13}A_{33} = -90$

(D) $a_{21}A_{21} = -24$

Choose the correct answer from the options given below:

$A=\begin{bmatrix} 0 & 1 & 3 \\ 1 & 2 & x \\ 2 & 3 & 1 \end{bmatrix}$ and $2B=\begin{bmatrix} 1 & -8 & 5 \\ -1 & 6 & -3 \\ 1 & 2y & 1 \end{bmatrix}$. If $A=B^{-1}$ then $x+y$ is equal to

If $A = \begin{bmatrix} 4 & 5 \\ 2 & 1 \end{bmatrix}$ and $I$ is an identity matrix of order 2, then $A - 3I$ equals

The value of $\Delta = \begin{vmatrix} 2\sin40^\circ & 2\sin50^\circ \\ -3\cos40^\circ & 3\cos50^\circ \end{vmatrix}$ is:

If $A = [a_{ij}]_{3 \times 3}$ and $a_{ij} = i - j$, then which of the following statements are TRUE?

(A). $A$ is scalar matrix

(B). $A$ is skew symmetric matrix

(C). $|A| = 0$

(D). $a_{21} + a_{12} = 0$

Choose the correct answer from the options given below:

If A is a square matrix of order 3 such that $|A|=2$, then the value of $|adj(adj A)|$ is :

The inverse of the matrix $\begin{bmatrix} 4 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 6 \end{bmatrix}$ is