If $\begin{vmatrix}x+1 & x-1 \\ x-3 & x+2\end{vmatrix}$ = $\begin{vmatrix}4 & -1 \\ 1 & 3\end{vmatrix}$ , then write the value of x.

If $A_{i j}$ is the cofactor of the element $a_{i j}$ of the determinant $\begin{vmatrix}2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7\end{vmatrix}$ , then write the value of $a_{32}A_{32}.$

If A is square matrix of order 2 and $|a d j A|=9,$ , find | A |.

If A is a square matrix and | A | = 2, then write the value of | AA’ |, where A’ is the transpose of matrix A.

If A = $\left(\begin{array}{l l }3 & 10 \\ 2 & 7\end{array}\right)$ , then write A⁻¹.

If A is a square matrix of order 3 such that $|a d j\,A|$ = 225, find $|A^{\prime}|.$

Write the inverse of the matrix $\left(\begin{array}{l l }cosθ & -sinθ \\ sinθ & cosθ\end{array}\right)$ .

The value of the determinant of a matrix A of order 3 × 3 is 4. Find the value of |5A|.

Is A is square matrix of order 3 and |2A| = k|A|, then find the value of k.

If the determinant of matrix A of order 3 × 3 is of value 4, write the value of |3A|.

Write the value of the determinant : $\begin{vmatrix}102 & 18 & 36 \\ 1 & 3 & 4 \\ 17 & 3 & 6\end{vmatrix}$

For what value of x, the matrix $\left(\begin{array}{l l }1+x & 7 \\ 3-x & 8\end{array}\right)$ is a singular matrix ?

If Δ = $\begin{vmatrix}5 & 3 & 8 \\ 2 & 0 & 1 \\ 1 & 2 & 3\end{vmatrix}$ , write the minor of the element $a_{23}.$

Write the value of $\begin{vmatrix}2 & 7 & 65 \\ 3 & 8 & 75 \\ 5 & 9 & 86\end{vmatrix}$

If A = $[a_{i j}]$ is is a matrix of order 2 × 2, such that |A| = –15, and $C_{i j}$ represents the cofactor of $a_{i j}$ , then find $a_{21}c_{21}+a_{22}c_{22}$