Matrices and Determinants jee mains questions | JEE Main Maths Matrices and Determinants Previous Year Question

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Q 31 :

Let A be a $3 \times 3$ matrix such that $A + A^{T} = O$ . If $A [\begin{matrix} 1 \\ - 1 \\ 0 \end{matrix}] = [\begin{matrix} 3 \\ 3 \\ 2 \end{matrix}], A^{2} [\begin{matrix} 1 \\ - 1 \\ 0 \end{matrix}] = [\begin{matrix} - 3 \\ 19 \\ - 24 \end{matrix}],$ and
$de t (a dj (2 adj (A + I))) = {(2)}^{α} \cdot {(3)}^{β} \cdot {(11)}^{γ},$ $α, β, γ$ are non-negative integers, then $α + β + γ$ is equal to _________ . [2026]

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