Test Questions

Test 3 #9

Proof: If $A$ is similar to $B$ then $A^2$ is similar to $B^2$.

$A=PBP^{-1}$
$A^2=AA=PBP^{-1}A$
$A^2=PBP^{-1}(PBP^{-1})$
$A^2=PBBP^{-1}$
$A^2=PB^{2}P^{-1}$

Therefore, $A^2$ is similar to $B^2$

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