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Math Help - [SOLVED] Finding a determinant (matrix)

  1. #1
    MHF Contributor arbolis's Avatar
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    [SOLVED] Finding a determinant (matrix)

    I just don't know how to start, so I'd like a push.
    Let A and B be 2\times 2 matrices that satisfies A^2B=3I and A^TB^3=-I, where I is the identity matrix. Calculate \det(A).
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    Moo
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    Hello !
    Quote Originally Posted by arbolis View Post
    I just don't know how to start, so I'd like a push.
    Let A and B be 2\times 2 matrices that satisfies A^2B=3I and A^TB^3=-I, where I is the identity matrix. Calculate \det(A).
    \text{det}(A^T)=\text{det}(A) and \text{det}(AB)=\text{det}(A) \times \text{det}(B)
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    MHF Contributor arbolis's Avatar
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    and
    ah.... the basic properties of the determinant.
    I reached \det(A)=-4 and \det(B)=-1. If you have time to check out the answer, I'd be glad. Otherwise it doesn't matter that much.
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