How to best tex this long matrix multiplication?

How to best tex this long matrix multiplication?

I have a quite large matrix multiplication:
\begin{align*}
\mathrm{Var}(\alpha)&\approx
\begin{pmatrix}\sqrt{1+\pi^{2}}\exp(-\delta^{*}+\zeta^{*})
&\frac{\pi\exp(-\delta^{*}+\zeta^{*})}{\sqrt{1+\pi^{2}}}&-\sqrt{1+\pi^{2}}\exp(-\delta^{*}+\zeta^{*})\end{pmatrix}
\begin{pmatrix} \mathrm{Var}(\zeta^{*}) &\mathrm{Cov}(\zeta^{*},\pi) &
\mathrm{Cov}(\zeta^{*},\delta^{*}) \\\mathrm{Cov}(\pi,\zeta^{*}) &
\mathrm{Var}(\pi) & \mathrm{Cov}(\pi, \delta^{*})
\\\mathrm{Cov}(\delta^{*},\zeta^{*}) & \mathrm{Cov}(\delta^{*},\pi) &
\mathrm{Var}(\delta^{*}) \end{pmatrix}
\begin{pmatrix}\sqrt{1+\pi^{2}}\exp(-\delta^{*}+\zeta^{*})
\\\frac{\pi\exp(-\delta^{*}+\zeta^{*})}{\sqrt{1+\pi^{2}}}\\-\sqrt{1+\pi^{2}}\exp(-\delta^{*}+\zeta^{*})\end{pmatrix}
\end{align*}
Since this does not fit a single line I am wondering how I could tex this
way in the best way? So that the logic of the matrix multiplication is
still visible?