jee-main 2025 Q15

jee-main · India · session1_23jan_shift2 Matrices Linear System and Inverse Existence
Let $A = \left[ a _ { i j } \right]$ be $3 \times 3$ matrix such that $A \left[ \begin{array} { l } 0 \\ 1 \\ 0 \end{array} \right] = \left[ \begin{array} { l } 0 \\ 0 \\ 1 \end{array} \right] , A \left[ \begin{array} { l } 4 \\ 1 \\ 3 \end{array} \right] = \left[ \begin{array} { l } 0 \\ 1 \\ 0 \end{array} \right]$ and $A \left[ \begin{array} { l } 2 \\ 1 \\ 2 \end{array} \right] = \left[ \begin{array} { l } 1 \\ 0 \\ 0 \end{array} \right]$, then $a _ { 23 }$ equals :
(1) $- 1$
(2) 2
(3) 1
(4) 0
Let $A = \left[ a _ { i j } \right]$ be $3 \times 3$ matrix such that $A \left[ \begin{array} { l } 0 \\ 1 \\ 0 \end{array} \right] = \left[ \begin{array} { l } 0 \\ 0 \\ 1 \end{array} \right] , A \left[ \begin{array} { l } 4 \\ 1 \\ 3 \end{array} \right] = \left[ \begin{array} { l } 0 \\ 1 \\ 0 \end{array} \right]$ and $A \left[ \begin{array} { l } 2 \\ 1 \\ 2 \end{array} \right] = \left[ \begin{array} { l } 1 \\ 0 \\ 0 \end{array} \right]$, then $a _ { 23 }$ equals :\\
(1) $- 1$\\
(2) 2\\
(3) 1\\
(4) 0