Let $G$ be an elementary abelian p-group of order $p^{2}$. Let $g$, $h$ be two non-trivial elements of $G$. I want to construct an automorphism $\phi\in Aut(G)$ such that $\phi(h)=g$, which is equivalently to give an invertible matrix $\left( \begin{array}{cc} a_{11} & a _{12} \\ a_{21} & a_{22}% \end{array}% \right)\in GL_{2}(\mathbb{F}_{p})$ such that $$\left( \begin{array}{cc} a_{11} & a _{12} \\ a_{21} & a_{22}% \end{array}% \right)\left( \begin{array}{c} a \\ b % \end{array}% \right)=\left( \begin{array}{c} a' \\ b' % \end{array}% \right) $$
for $h=\left( \begin{array}{c} a \\ b % \end{array}% \right) $ and $g=\left( \begin{array}{c} a' \\ b' % \end{array}% \right) $.
But I don't know what to do next to find $(a_{ij})_{1\leq i, j\leq2}$.
Thank you very much for any help.