1. ## det(A^4)=0

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

2. Originally Posted by ssl000
Suppose that A is a square matrix such that det A^4=0. Explain why A cannot be invertible.
Hint: $\displaystyle \text{det }A^4 = (\text{det }A)^4$

3. 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.

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

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### 3×0 = explain how.?

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