# Thread: Find A^2 = A * A, A^3 = A * A * A, A^4, and A^100, given

1. ## Find A^2 = A * A, A^3 = A * A * A, A^4, and A^100, given

that A equals

$\left[\begin{matrix}0&2&0\\0&0&2\\0&0&0\\0&0&0\end{matri x}\left|\begin{matrix}-1\\0\\2\\0\end{matrix}\right]$

2. To find $A^n$ you can firstly need to diagonalise $A$ for an example look here.

Diagonalization

3. thanks for the link but those symbols aren't in my textbook and therefore i can't understand it.

4. Ok, you may not need to know the symbols, just the ideas. Do you know how to find eigenvectors?

5. Actually, you can't diagonalize the matrix. However, it is upper-triangular. Finding the first few powers of $A$ should give a recognizable pattern.

6. Blast, roninpro got in ahead of me!

Yes, it is not necessary to diagonalize this matrix. Direct calculation gives $A^2$ and $A^3$ and shows that $A^4= 0$.