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Thread: det(A^4)=0

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

    Suppose that A is a square matrix such that det A^4=0. Explain why A cannot be invertible.
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  2. #2
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    Quote Originally Posted by ssl000 View Post
    Suppose that A is a square matrix such that det A^4=0. Explain why A cannot be invertible.
    Hint: $\displaystyle \text{det }A^4 = (\text{det }A)^4$
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  3. #3
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    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.
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  4. #4
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    Quote Originally Posted by ssl000 View Post
    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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