Let A be an n x n matrix.

a) Suppose that A^2 = O. Prove that A is not invertible

b) Suppose that AB = O for some nonzero n x n matrix B. Could A be invertible? Explain.

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- Oct 26th 2008, 05:54 PMleungstaInvertibility & Isomorphism
Let A be an n x n matrix.

a) Suppose that A^2 = O. Prove that A is not invertible

b) Suppose that AB = O for some nonzero n x n matrix B. Could A be invertible? Explain. - Oct 26th 2008, 08:08 PMThePerfectHacker
If $\displaystyle AA^{-1} = I \implies A^2A^{-1} = A \implies 0 = A$ a contradiction.

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b) Suppose that AB = O for some nonzero n x n matrix B. Could A be invertible? Explain.