(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let A be an nxn matrix such that A^k=0 for some natural integer k (0 is the nxn zero matrix). Show that I + A is invertible, where I is the nxn identity matrix.

2. Relevant equations

Invertible implies det(I+A) not equal zero.

3. The attempt at a solution

I really don't know where to start with this one. I can see that A itself must be non-invertible, but I can't seem to get any more conditions on A based on that fact that A^k=0. Could anyone give me a hint please?

Thanks.

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# Invertible matrices

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