Write the number of all possible matrices of order $2\times 2$ with each entry $1$, $2$ or $3$?

If $\mathrm{A}=\left[\begin{array}{cc}2& 4\\ 3& 2\end{array}\right], \mathrm{B}=\left[\begin{array}{cc}1& 3\\ -2& 5\end{array}\right]$ and $\mathrm{C}=\left[\begin{array}{cc}-2& 5\\ 3& 4\end{array}\right]$, find the following:

$\mathrm{A}+\mathrm{B}$

If $\mathrm{A}=\left[\begin{array}{cc}2& 4\\ 3& 2\end{array}\right], \mathrm{B}=\left[\begin{array}{cc}1& 3\\ -2& 5\end{array}\right]$ and $\mathrm{C}=\left[\begin{array}{cc}-2& 5\\ 3& 4\end{array}\right]$, find the following:

$\mathrm{A}-\mathrm{B}$

If $\mathrm{A}=\left[\begin{array}{cc}2& 4\\ 3& 2\end{array}\right], \mathrm{B}=\left[\begin{array}{cc}1& 3\\ -2& 5\end{array}\right], \mathrm{C}=\left[\begin{array}{cc}-2& 5\\ 3& 4\end{array}\right]$ find each of the following:

$3\mathrm{A}-\mathrm{C}$

Compute the following:

$\left[\begin{array}{cc}\mathrm{a}& \mathrm{b}\\ -\mathrm{b}& \mathrm{a}\end{array}\right]+\left[\begin{array}{cc}\mathrm{a}& \mathrm{b}\\ \mathrm{b}& \mathrm{a}\end{array}\right]$

Compute the following :

$\left[\begin{array}{cc}{\mathrm{a}}^2+{\mathrm{b}}^2& {\mathrm{b}}^2+{\mathrm{c}}^2\\ {\mathrm{a}}^2+{\mathrm{c}}^2& {\mathrm{a}}^2+{\mathrm{b}}^2\end{array}\right]+\left[\begin{array}{cc}2\mathrm{ab}& 2\mathrm{bc}\\ -2\mathrm{ac}& -2\mathrm{ab}\end{array}\right]$

Compute the following :

$\left[\begin{array}{ccc}-1& 4& -6\\ 8& 5& 16\\ 2& 8& 5\end{array}\right]+\left[\begin{array}{ccc}12& 7& 6\\ 8& 0& 5\\ 3& 2& 4\end{array}\right]$ 

Compute the following :

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