Bijective check with matrix My book doesn't cover the criterion for bijective transformations very well. I just want to check my understanding: is this statement true?

Let F be a linear transformation. Let A be the matrix that represents that transformation (which means that that $F(v)=Av$ for any vector $v$). We now have that F is bijective iff $\det(A)\not=0$.


I think about this in the following manner. A bijective linear transformation should have an inverse. Hence the associated matrix should also be invertible. Therefore it's determinant is non-zero. Hope this helps. 
