$T : R^{n\times m}\to R^{m\times m}$, $C \to (AC)^T$
I need to find the inverse of this linear transformation, when A is an invertible matrix... Can anyone help me with this problem?
I am asked to show that the transformation is bijective if A is inversible so I thought about using that a lin. transformation is bijective iff it has an inverse... maybe there is a better way
I realize that A has either a left or right inverse, and that both are a (n x m) matrix.
If B is the left inverse of A, I have figured that $S(X): B(X)^T$ is the inverse of T
Is that enough or do I also have to find a transformation assuming B is the right inverse of A?