- #1

- 138

- 0

## Homework Statement

**A**is nxn

**B**is nxp

Is the rank of

[

**B AB**...

**A**

^{n-1}

**B**]

equal to the rank of

[

**AB A**

^{2}

**B**...

**A**

^{n}

**B**]?

If not, under what condition will the ranks be equal?

## The Attempt at a Solution

I don't even know where to start. I know that both matrices should have the same number of pivots, but since this is so generalized I don't know how to learn anything about how multiplying by

**A**would change the number of pivots!

Can someone help me out and at least give me a hint? I've been staring at this for the longest time and just don't know what to do!

Thanks!