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Math Help - 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: \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.
    det A^4=0 means (det A)^4=0 so det A=0 and therefore A is not invertible.
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