proof that nxn matrix is invertible by showing null space of left hand multiplication matrix to equal 0

Question

If I want to show that an $n$ x $n$ matrix $A$ is invertible then why is it that $$N(L_A)=\{0\}$$ proves that $A$ is invertible? and $N(L_a)$ denotes the null space of the left hand matrix multiplication.

Thanks in advance!