MathsJEE Main 22 Jan 2026, Shift 1·Q22·Numerical·Tough

Matrices & Determinants · Adjoint and determinant properties

Let

A

be a

3 \times 3

matrix such that

A + A^T = O

. If

A\begin{bmatrix} 1\\ -1\\ 0\end{bmatrix} = \begin{bmatrix} 3\\ 3\\ 2\end{bmatrix},\quad A^2\begin{bmatrix} 1\\ -1\\ 0\end{bmatrix} = \begin{bmatrix} -3\\ 19\\ -24\end{bmatrix}

and

\det(\operatorname{adj}(2\operatorname{adj}(A + I))) = (2)^{\alpha}\cdot(3)^{\beta}\cdot(11)^{\gamma}

,

\alpha, \beta, \gamma

are non-negative integers, then

\alpha + \beta + \gamma

is equal to .

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