Let \(A=\left[a_{i j}\right]\) be a \(3 \times 3\) matrix such that \(\mathrm{A}\left[\begin{array}{l}0 \\ 1 \\ 0\end{ar…

Let \(A=\left[a_{i j}\right]\) be a \(3 \times 3\) matrix such that \(\mathrm{A}\left[\begin{array}{l}0 \\ 1 \\ 0\end{array}\right]=\left[\begin{array}{l}0 \\ 0 \\ 1\end{array}\right], \mathrm{A}\left[\begin{array}{l}4 \\ 1 \\ 3\end{array}\right]=\left[\begin{array}{l}0 \\ 1 \\ 0\end{array}\right]\) and \(\mathrm{A}\left[\begin{array}{l}2 \\ 1 \\ 2\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]\), then \(\mathrm{a}_{23}\) equals:

[JEE Main 2025, 23 Jan (Shift 2)]