Answer
$T$ is a linear transformation.
Work Step by Step
$T$ is said to be a linear transformation, if for all $v,w$ in the given domain and for all scalars $a$,
$T(av+w)=aT(v)+T(w)$
Let $A_1$, $A_2$ be two arbitrary elements of the domain $M_{n,n}$ and $a$ be any scalar.
Then, $T(aA_1+A_2)=(aA_1+A_2)B\\
=aA_1B+A_2B\\
=a(A_1B)+(A_2B)\\
=aT(A_1)+T(A_2)$
Since, $A_1,A_2$ and $a$ are arbitrary, $T$ is a linear transformation.
