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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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up vote 5 down vote accepted

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 $(A+B)^n$

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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.

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