Are the two matrices similar? If so, find a matrix P such that B = P−1AP. (If not possible, enter IMPOSSIBLE.)A = 2 0 0 0 1 00 0 3 B = 1 0 0 0 2 00 0 3

Question

Are the two matrices similar? If so, find a matrix P such that B = P−1AP. (If not possible, enter IMPOSSIBLE.)

A =
$\begin{pmatrix} 2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 3 \end{pmatrix}$

B =
$\begin{pmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{pmatrix}$

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Solution

Two matrices A and B are said to be similar if there exists an invertible matrix P such that B = P^-1 * A * P.

Given matrices A and B are:

A = [2 0 0; 0 1 0; 0 0 3] B = [1 0 0; 0 2 0; 0 0 3]

We can see that the diagonal elements of A and B are not the same, which means that A and B are not similar. Therefore, it is IMPOSSIBLE to find a matrix P such that B = P^-1 * A * P.

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Are the two matrices similar? If so, find a matrix P such that B = P−1AP. (If not possible, enter IMPOSSIBLE.)A = 2 0 0 0 1 00 0 3 B = 1 0 0 0 2 00 0 3

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