I would love some guidance on how I should approach this question:

Question: If A is an idempotent matrix of order n, show that $\displaystyle (I+A)^n = I+(2^N-1)A$

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- Feb 20th 2011, 04:18 PMsparkyIdempotent Matrix
I would love some guidance on how I should approach this question:

Question: If A is an idempotent matrix of order n, show that $\displaystyle (I+A)^n = I+(2^N-1)A$ - Feb 20th 2011, 06:38 PMtonio
- Feb 23rd 2011, 04:03 PMsparky
Thank you for your reply Tonio.

I am still trying to figure out how to show in your first point.

Here is what I understand so far:

A matrix $\displaystyle A$ is said to be idempotent if $\displaystyle A^2=A$ - Feb 23rd 2011, 06:06 PMtonio

Well, understanding definitions is important but it's hardly enough for this problem...

Further hint:

For any pair of commuting elements a,b in a ring and for*Newton's Binomial Theorem:*

any natural n, we have that $\displaystyle \displaystyle{(a+b)^n=\sum\limits^n_{k=0}\binom{n} {k}a^{n-k}b^k}$

Tonio