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QUESTION

The $n\times n$ matrices $A$ and $B$ are called similar if
$B=M^{-1}AM$ for some invertible M. Show that in this case $\det
A=\det B$.

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ANSWER

$\det(M^{-1}AM)=\det M^{-1}\times\det A\times\det M= (\det
M)^{-1}\times\det A\times\det M=\det A$.




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