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  1. #1
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    matrices problem...

    Q:let A and B be real matrices such that sum of each row of A is 1 and sum of each row of B is 2.then show that 2 is an eigen value of AB?
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  2. #2
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    Quote Originally Posted by Mathventure View Post

    let A and B be \color{red}n \times n real (we don't need this assumption!) matrices such that sum of the entries in each row of A is 1 and sum of the entries in each row of B is 2.

    then show that 2 is an eigenvalue of AB?
    let x=\begin{bmatrix}1 & 1 & . & . & . & 1 \end{bmatrix}^T. then Ax=x and Bx=2x. thus (AB)x=A(2x)=2Ax=2x.
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