Dadas as matrizes A=\left[\begin{array}{ccc}t & 0 & 1 \\\\ 0 & 1 & 5 \\\\ 3 & 0 & 1\end{array}\right] e B=\left[\begin{array}{lll}2 & 2 & 2 \\\\ 0 & s & 2 \\\\ 1 & 1 & 2\end{array}\right], com t, s \in \mathbb{R} fixados tais que t \neq 3 e s \neq 0, calcule o determinante de: B^{-1} A^{2}.