For any square matrix $A=[a_{ij}],a_{ij}=0$, when $i\ne j$, then $A$ is

We have, $a_{ij}=0$ when $i\ne j$
That mean all the non diagonal elements of the matrix are zero,
So the matrix is,
$A=\left[\begin{array}{ccccc}{a}_{11}& 0& 0& ...........& 0\\ 0& a_{22}& 0& .......& 0\\ 0& 0& a_{33}& ....& 0\\ & & & & \\ & & & & \\ & & & & \\ 0& 0& 0& .........& a_{nn}\end{array}\right]$, where $n$ is order of the matrix
Clearly $A$ is a diagonal matrix