Matrix Addition

${\displaystyle \left[{\begin{array}{ccc}0&0&1\\0&1&1\\1&0&1\\\end{array}}\right]+\left[{\begin{array}{ccc}0&1&1\\1&0&0\\1&1&1\\\end{array}}\right]=\left[{\begin{array}{ccc}0&1&2\\1&1&1\\2&1&2\\\end{array}}\right]}$

${\displaystyle \left[{\begin{array}{cc}a&b\\c&d\\\end{array}}\right]+\left[{\begin{array}{cc}p&q\\r&s\\\end{array}}\right]=\left[{\begin{array}{cc}a+p&b+q\\c+r&d+s\\\end{array}}\right]}$

Matrix Multiplication

${\displaystyle A\times I=I\times A=A}$

${\displaystyle A\times I=\left[{\begin{array}{cc}a&b\\c&d\\\end{array}}\right]\times \left[{\begin{array}{cc}1&0\\0&1\\\end{array}}\right]=\left[{\begin{array}{cc}1\times a+0\times b&0\times a+1\times b\\1\times c+0\times d&0\times c+1\times d\\\end{array}}\right]=\left[{\begin{array}{cc}a&b\\c&d\\\end{array}}\right]=A}$

${\displaystyle \left[{\begin{array}{ccc}0&0&1\\0&1&1\\1&0&1\\\end{array}}\right]+\left[{\begin{array}{ccc}0&1&1\\1&0&0\\1&1&1\\\end{array}}\right]=\left[{\begin{array}{ccc}0&1&2\\1&1&1\\2&1&2\\\end{array}}\right]}$