Question

How do you add $2\times 2$ matrices?

Answer 1

Addition of two matrices can be done by addition of Corresponding terms of the matrices only if both the matrices are of same size.

Let us take an example:

$A=\left[\begin{array}{cc}4& 8\\ 3& 7\end{array}\right]$

Dimensions of matrix $A$is $2\times 2$

$B=\left[\begin{array}{cc}1& 0\\ 5& 2\end{array}\right]$

Dimensions of matrix $B$ is $2\times 2$

$\begin{array}{rcl}A+B& =& \left[\begin{array}{cc}\left(4+1\right),& \left(8+0\right)\\ (3+5),& (7+2)\end{array}\right]\\ A+B& =& \left[\begin{array}{cc}5& 8\\ 8& 9\end{array}\right]\end{array}$ Adding corresponding elements

Hence, the way to add $2\times 2$ matrix is just to ad the corresponding elements as shown above.