Hello,

Problem:

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 ".

My effort:

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?

Thank you,

Srikanth