Let A be a 3×3 matrix such that A+A^(T)=O. If A 1 -1 0 = 3 3 2, A² 1 -1 0 = -3 19 -24 and det (adj(2 adj(A+I)))=(2)^(α)·(3)^(β)·(11)^(γ), α, β, γ are non-negative integers, then α+β+γ is equal to

Matrices and Determinants: JEE Main 2026 Mathematics question

JEE Main 2026 · 22 Jan, Morning shift · Q24

JEE Main 202622 Jan, Morning shiftMathematicsHardMatrices and Determinants245× since 2002

Let A be a

3\times3

matrix such that

\mathrm{A}+\mathrm{A}^{\mathrm{T}}=\mathrm{O}

. If

\mathrm{A}\begin{bmatrix}1\\-1\\0\end{bmatrix}=\begin{bmatrix}3\\3\\2\end{bmatrix}

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

and

\det(\mathrm{adj}(2\,\mathrm{adj}(\mathrm{A}+\mathrm{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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