Identity matrix

The identity matrix of size $n$ is an $n\times n$ square matrix where all of the values in its main diagonal are ones and all other values are zeroes. Alternatively, an identity matrix is a square diagonal matrix whose diagonal is one in every position. For example, the identity matrix of size 3 is

${\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}}$

The identity matrix of size $n$ is the identity element of all invertible matrices of size $n\times n$ .