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## Homework Statement

If A

^{100}is some 3x3 matrix, find the base matrix A.

**2. Relevant information**

Eigenvalues, diagonalization, etc.

## The Attempt at a Solution

So far, I've been finding the eigenvalues and diagonalizing the matrix via A = P

^{-1}DP where D is the diagonal matrix and P is a matrix with A's eigenvalues. hoping to find the base matrix with powers of n. Any suggestions to guide me?

There was a similar discussion to this earlier, trying to reference that as well.