If A,B,C,D are matrices such that C and D commute and D is invertible, then
There is a hint that says " multiply on the right by ".
So I observed that:
If we choose , then
Now since C and D commute, . Thus
It looked like a convincing proof until I realised that I have used the hypothesis in the penultimate step. I have also used it while setting .
So how can I fix those steps? Or do we need a different direction?