# Do you Know Matrices ?

Algebra Level pending

$$\displaystyle A$$ 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.

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