Proposition (Injectivity, surjectivity, and isomorphism are equivalent when dimension is the same)

IF $V,W$ are finite dimensional vector spaces such that $dim(V)=dim(W)$, and we have some Linear Map $T\in\mathscr{L}(V,W)$, then the following are equivalent: 1. $T$ is Injective 2. $T$ is Surjective 3. $T$ is invertible