TITLE: Binomial theorem for matrices
QUESTION [11 upvotes]: Suppose we have
$$(A + I)^n$$
where $A$ is matrix and $I$ is an identity matrix. Does the binomial theorem apply?
I know the binomial theorem but not whether it is also applicable to matrices.

REPLY [10 votes]: Think about how binomial theorem is proved. You would quickly realize that the theorem can be proved by the same way for $(A+B)^n$ if $A$ and $B$ commute.