Let \(A=\left[\begin{matrix}1 & 0 & 0 \\ 3 & 1 & 0 \\ 9 & 3 & 1\end{matrix}\right]\) and \(B=\left[{b}_{ij}\right],1\leq…

Let \(A=\left[\begin{matrix}1 & 0 & 0 \\ 3 & 1 & 0 \\ 9 & 3 & 1\end{matrix}\right]\) and \(B=\left[{b}_{ij}\right],1\leq i,j\leq 3\). If \(B={A}^{99}-I\), then the value of \(\frac{b_{31}-b_{21}}{b_{32}}\) is:

[JEE Main 2026, 6 Apr (Shift 2)]