Let $A = [a_{ij}]_{2\times 2}$, where $a_{ij}\ne 0$ for all $i,j$ and $A^{2}=I$. Let $a$ be the sum of all diagonal elements of $A$ and $b=\lvert A\rvert$ (i.e., $b=\det A$). Then $3a^{2}+4b^{2}$ is equal to: