If $A = \begin{bmatrix} 4 & x + 2 \\ 2x - 3 & x + 1 \end{bmatrix}$ is a symmetric matrix,then $x = $

If $A = \begin{bmatrix} 1 & 2 & 3 \\ -2 & 3 & -1 \\ 3 & 1 & 2 \end{bmatrix}$ and $I$ is a unit matrix of $3^{rd}$ order,then $(A^2 + 9I)$ equals

Let $A = \begin{bmatrix} 2 & 4 \\ 3 & 2 \end{bmatrix}$,$B = \begin{bmatrix} 1 & 3 \\ -2 & 5 \end{bmatrix}$,and $C = \begin{bmatrix} -2 & 5 \\ 3 & 4 \end{bmatrix}$. Find $A - B$.

If $A = \text{diag}(2, -1, 3)$ and $B = \text{diag}(-1, 3, 2)$,then $A^2B = $

If $A=\left[\begin{array}{rrr}1 & 1 & -1 \\ 2 & 0 & 3 \\ 3 & -1 & 2\end{array}\right]$,$B=\left[\begin{array}{rr}1 & 3 \\ 0 & 2 \\ -1 & 4\end{array}\right]$ and $C=\left[\begin{array}{rrrr}1 & 2 & 3 & -4 \\ 2 & 0 & -2 & 1\end{array}\right]$,find $A(BC)$,$(AB)C$ and show that $(AB)C=A(BC)$.

Find $AB,$ if $A=\left[\begin{array}{ll}6 & 9 \\ 2 & 3\end{array}\right]$ and $B=\left[\begin{array}{lll}2 & 6 & 0 \\ 7 & 9 & 8\end{array}\right].$