If $a_{ij}=0\left(i\ne j\right)$ and $a_{ij}=1\left(i=j\right)$ then the matrix A= ${\left[a_{ij}\right]}_{n\times n}$ is a _____ matrix

The elements $a_{ij}$ of a matrix where $i=j$ lie along its diagonal and the elements $a_{ij}$ of a matrix where $i\ne j$ are not along the diagonal. As the diagonal elements are $1$ and the rest of the elements are $0$, the matrix $A$ is an identity matrix.