# Linear Algebra - linear transformation isomorphism true/false question

Let $R^3 \rightarrow R^3$ linear transformation that defined $T_A(v)=Av$ is it isomorphism?

I'm not sure but it seems like it the identity transformation, Therefore I think it isomorphism, but the answer says no,

Any idea?, Thanks

It's only isomorphic if $A$ is nonsingular. Consider $A=0$.