Answer
See below
Work Step by Step
Take $A \in M_2(R)\\
c \in R$
$T: M_2(R)\rightarrow R$ defined by
$T(A)=\det (A)$
We obtain:
$$T(c(A))=\det(A)=c^2A\\
cT(A)=cA\\
\rightarrow T(c(A))\ne cT(A)$$
Thus it is not a linear transformation.