I'm learning linear algebra, and I understand that a linear transformation is represented by a matrix. So the following $T: \Bbb R^n \rightarrow \Bbb R^n $ can be represented as $ \mathbf Ax = b $, where A is square.
I also understand that you can find A from x and b by using them in a system of equations with the basis vectors.
However, how do you to find $ \mathbf A$ if both x and b are rectangular matrices?
The only instruction I found suggests inverting $x$, which is impossible since the matrix is not possible in a non square matrix? Is it only possible to find $ \mathbf A $ if $x$ and $b$ are both square?
For example suppose I have the linear transformation:
$$ \mathbf A\begin{bmatrix} 0.6 && 0.2 && 0.2 \\ 0.5 && 0.3 && 0.1 \end{bmatrix} = \begin{bmatrix} 0.9 && 0.05 && 0.05 \\ 1 && 0 && 0 \end{bmatrix} $$