If P is a fixed n $\backslash$times n matrix, then the similarity transformation

A$->$P $1$

AP

can be viewed as an operator SP $($A$)=$ P $1$

AP on the vector

space Mnn of n $\backslash$times n matrices.

$($a$)$ Show that SP is a linear operator.

$($b$)$ Find the kernel of SP $.$

$($c$)$ Find the rank of SP $.$