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Math Help - Invertible matrix question

  1. #1
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    Question Invertible matrix question

    Let A 2 R^n x n and α belongs to R. Show that the matrix A-αI is invertible if, and only if, the matrix A^ T - αI is invertible, where I is the identity matrix.

    Please help!!! have no idea to do this question.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by gklove56 View Post
    Let A 2 R^n x n and α belongs to R. Show that the matrix A-αI is invertible if, and only if, the matrix A^ T - αI is invertible, where I is the identity matrix.

    Please help!!! have no idea to do this question.
    This would be clear if we knew these two matrices have the same eigenvalues. Do we? If so, how?
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