[ 0 0 1 0 1 1 1 0 1 ] + [ 0 1 1 1 0 0 1 1 1 ] = [ 0 1 2 1 1 1 2 1 2 ] {\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]}
[ a b c d ] + [ p q r s ] = [ a + p b + q c + r d + s ] {\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]}
A × I = I × A = A {\displaystyle A\times I=I\times A=A}
A × I = [ a b c d ] × [ 1 0 0 1 ] = [ 1 × a + 0 × b 0 × a + 1 × b 1 × c + 0 × d 0 × c + 1 × d ] = [ a b c d ] = 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]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/38d3720eb5edc28d102a0c0d317afe3ed0390b1a)
![{\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]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d870e2a9efecf7d66ab795912d5506a2deb3ab4f)
![{\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}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c02f86b07bb335f6e21bdf9d3fad3d263ca80ceb)
