Strong Induction: Prove $a_n=(-3)^n$ I need help with the following problem.

$a_0=1$
$a_1=-3$
$a_n=-2*a_{n-1}+3*a_{n-2}$, for all $n\ge2$
prove $a_n=(-3)^n$

I understand the base cases, I'm just confused on how to do the strong induction step. I know that we are showing that if P(n) is true then it must hold for P(n+1) but I don't know how to do that with $a_{n+1}$

Substitute in the induction hypothesis for $a_{n}$ and $a_{n-1}$ to get:
\begin{eqnarray}
a_{n+1} &=& -2 a_n + 3 a_{n-1}\\
 &=& -2(-3)^{n} + 3(-3)^{n-1}\\
 &=& -2(-3)^n -(-3)^n\\
 &=& -3(-3)^n\\
 &=& (-3)^{n+1}
\end{eqnarray}
