Question

If A and B are invertible matrices of order 3, $|\mathbf{A}|=$ 2 and $|(\mathbf{AB})^{-1}|\,=\,-{\frac{1}{6}}.$ Find $|\mathbf{B}$.

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

If $\left(\begin{array}{l l }2 & 3 \\ 5 & 7\end{array}\right)$ $\left(\begin{array}{l l }1 & -3 \\ -2 & 4\end{array}\right)$ = $\left(\begin{array}{l l }-4 & 6 \\ -9 & x\end{array}\right)$ , write the value of x.

If matrix A = [1 2 3], then write AA’.

Write the number of all possible matrices of order 2 × 2 with each entry 1, 2 or 3.

Give an example of a skew symmetric matrix of order 3.

If A is an invertible square matrix of order 3 and |A| = 5, then find the value of |adj A|.