An identity matrix can be written as [a_ij]_n×n where,

$aij=\left\{\begin{matrix}0, & when & i≠j \\k, & when & i=j \end{matrix}\right.$

$aij=\left\{\begin{matrix}0, & when & i≠j \\1, & when & i=j \end{matrix}\right.$

$aij=\left\{\begin{matrix}k, & when & i≠j \\0, & when & i=j \end{matrix}\right.$

$aij=\left\{\begin{matrix}1, & when & i≠j \\0, & when & i=j \end{matrix}\right.$