Do you Know Matrices ?

$\displaystyle A$ is the $\displaystyle n \times n$ matrix whose elements are all $\displaystyle '1'$ and $\displaystyle B$ is the $\displaystyle n \times n$ matrix whose diagonal elements are all $\displaystyle 'n'$ and other elements are $\displaystyle 'n-r'$ . Then $\displaystyle A^{2}$ is a scalar multiple of A and hence , $\displaystyle ( B-rI)[B - (n^{2}-nr+R)I]$ is ? Here $\displaystyle I$ is the Identity matrix.