Prove that if a square matrix A is similar to a scalar matrix (lambda)I, then A=(lambda)I.

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- Jul 26th 2009, 03:46 PMbethhsimilar matrices
Prove that if a square matrix A is similar to a scalar matrix (lambda)I, then A=(lambda)I.

- Jul 26th 2009, 04:26 PMRandom Variable
$\displaystyle A = P^{-1} (\lambda I) P = P^{-1}\lambda (IP)= P^{-1}\lambda P = \lambda (P^{-1}P)=\lambda I$