Australian Curriculum Mathematics/General Mathematics

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

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

Matrix Multiplication
$$A\times I=I\times A=A$$

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

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