# Thread: I need a hint!

1. ## I need a hint!

Hi, I have uploaded a picture that shows my question. Can someone give me a direction, I have been sitting on this for hours, I couldn't do it. I tried to use the fact that P and Q are invertible and tried to find A in block matrix and maybe somehow get something, I am trying random things, I don't really know what I am doing, so can someone give me a subtle hint, by that I mean a hint that doesn't show me what to do in every step of the solution but rather gives me a first step how to start solving it. Thank you.

2. ## Re: I need a hint!

Row-reduce A, which will give you P as a product of elementary row-operation matrices.

Column reduce rref(A) (row-reduced echeclon form of A), which will "diagonalize" the pivot columns giving you Q as a product of elementary column operations (which will be transposes of elementary row-operation matrices).

What is your guess on the relationship between the size of I, and the rank of A?

3. ## Re: I need a hint!

Thank you Deveno! The problem that I couldn't do it because I thought they wanted a specific number for I and I didn't how that was possible, I thought there was a trick or something, but it was an easy question after all.