605-Discussion 3

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Eigenvalues

T17† Suppose that B is a nonsingular matrix. Prove that AB is similar to BA.

Non singular (invertible)=> \(B^{-1}B = 1 = I{n}\) , therefore:

\[ AB = B^{-1}BAB = B^{-1}(BA)B = I{n}BA = BA \]