Suppose that A is a square matrix such that det A^4=0. Explain why A cannot be invertible.

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Originally Posted by ssl000 Suppose that A is a square matrix such that det A^4=0. Explain why A cannot be invertible. Hint:

I know of the theorem, det(AB)=det(A)*det(B). det(A^4)=det(A)*det(A)*det(A)*det(A) will equal to zero, making it invertible, but I still don't understand why it will equal to zero.

Originally Posted by ssl000 Suppose that A is a square matrix such that det A^4=0. Explain why A cannot be invertible. means so and therefore is not invertible.

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