Math Help - Linear Algebra matrix to a general power

1. Linear Algebra matrix to a general power

What kinds of numbers will be found as entries in $A^n$? (n-any positive integer) What kinds of numbers are impossible?

No idea how to approach this one.

2. Re: Linear Algebra matrix to a general power

here is a place to start: suppose that the entries of A are integers. will the entries of A^n be non-integers?

another example: suppose that the entries of A are rational. will the entries of A^n ever be irrational?