Binomial theorem for matrices

Question

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.

Answer 1

Sure. You could prove it the same way. It works because there is no difficulty about elements commuting in the case you have chosen. But it would not work for $(A+B)^n$

Answer 2

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.