) numbers whose product is independent of the order of the factors. An example of two matrices not commuting with each other is:[1234][0100]=[0103],{\displaystyle {\begin{bmatrix}1&2\\3&4\\\end{bmatrix}}{\begin{bmatrix}0&1\\0&0\\\end{bmatrix}}={\begin{bmatrix}0&1\\0&3\\\end{bmatrix}},}whereas[0100][1234]=[3400].{\displaystyle {\begin{bmatrix}0&1\\0&0\\\end{bmatrix}}{\begin{bmatrix}1&2\\3&4\\\end{bmatrix}}={\begin{bmatrix}3&4\\0&0\\\end{bmatrix}}.}The identity matrix In of size n is the n-by-n matrix in which all the elements on the main diagonal are equal to 1 and all other elements are equal to 0, e.g.I3=[100010001].{\displaystyle \mathbf {I} _{3}={\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}}.}It is called identity matrix because multiplication with it 