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Math Help - Rank and Determinant of A*B matrix

  1. #1
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    Rank and Determinant of A*B matrix

    Would someone please instruct me how to show if

    det(AB) = det(BA)

    Also, how should I show if rank(A)rank(B) is equal to rank(AB) or not.
    rank(AB)=rank(A)rank(B)

    Thank you.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Rank and Determinant of A*B matrix

    Quote Originally Posted by itpro View Post
    Would someone please instruct me how to show if det(AB) = det(BA)
    \det(AB)=\det(A)\det(B)=\det(B)\det(A)=\det(BA)

    Also, how should I show if rank(A)rank(B) is equal to rank(AB) or not.
    It is false, choose for example A=\begin{bmatrix}{0}&{1}\\{0}&{0}\end{bmatrix} \quad B=\begin{bmatrix}{0}&{2}\\{0}&{0}\end{bmatrix}
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