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Let $A$ be a square matrix such that $A^2 = A$. Any idea how to show that $A$ cannot be a strictly diagonally dominated matrix unless $A$ is the identity matrix.

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Well, what do you know about "strictly diagonally dominated" matrices? Any theorems? – Gerry Myerson Mar 4 '12 at 22:56

Write the equality as $A(A-I)=0$ and use the fact that strictly diagonally dominated matrices are invertible (you can prove that, right?) to eliminate $A$.

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