# Binomial Theorem on a Matrix

Does the expression follow binomial theorem?

$(A + I)^n$ where $A$ is matrix, $I$ is identity matrix. I know the binomial theorem but do not know whether it is applicable to matrices also.

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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 $(A+B)^n$
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.