How can (if at all) the below matrix be factorized?

Question

Suppose we have the matrix \begin{equation} \begin{bmatrix} ac &ad\\ be & bf \end{bmatrix} \end{equation} Is there anyway to factor out $a$ and $b$?

Answer 1

You could write this as $$\left[\matrix{a & 0\cr 0 & b\cr}\right] \left[\matrix{c & d\cr e & f\cr}\right]$$ if that's what you mean.