If two matrices have the same determiant, are they similar? – math.stackexchange.com

If two matrices have the same determiant, are they similar? – math.stackexchange.com

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I am wondering if we have two square matrices $A$ and $B$ and if $\det A = \det B$, then does an invertible matrix $P$ exist with $$A = P^{-1} B P$$

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