Let $A$ and $B$ be two symmetric matrices of the same order. Then, the matrix $AB - BA$ is

If $A = \begin{bmatrix} 2 & -1 \\ -1 & 2 \end{bmatrix}$ and $I$ is the unit matrix of order $2$,then $A^2$ equals

If $A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$,then $AB = $

Compute the following: $\left[ {\begin{array}{cc} {{\cos }^2}x & {{\sin }^2}x \\ {{\sin }^2}x & {{\cos }^2}x \end{array}} \right] + \left[ {\begin{array}{cc} {{\sin }^2}x & {{\cos }^2}x \\ {{\cos }^2}x & {{\sin }^2}x \end{array}} \right]$

If $m[-3, 4] + n[4, -3] = [10, -11]$, then $3m + 7n$ is equal to

Express the following matrix as the sum of a symmetric and a skew-symmetric matrix: $\left[\begin{array}{ccc}3 & 3 & -1 \\ -2 & -2 & 1 \\ -4 & -5 & 2\end{array}\right]$