I would love some guidance on how I should approach this question:
Question: If A is an idempotent matrix of order n, show that $\displaystyle (I+A)^n = I+(2^N-1)A$
Well, understanding definitions is important but it's hardly enough for this problem...
Further hint:
Newton's Binomial Theorem: For any pair of commuting elements a,b in a ring and for
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