Let A be a 3 \times 3 matrix such that A + A ^{ T }= O. If A \left[\begin{array}{c}1 \ -1 \ 0]\end{array}=\left[\begin{array}{c}3 \ 3 \ 2]\end{array}, A ^2\left[\begin{array}{c}1 \ -1 \ 0]\end{array}=\left[\begin{array}{c}-3 \ 19 \ -24]\end{array} and {\det}({\adj}(2 {\adj}(A+ I )))=(2)^\alpha \cdot(3)^\beta \cdot(11)^\gamma, \alpha, \beta, \gamma are nonnegative integers, then \alpha+\beta+\gamma is equal to \_\_\_\_ [22 Jan 2026 Shift 1]

Matrices and Determinants Part 4

Section: Mathematics

Question : 13 of 58

Marks: +1, -0

Let A be a 3×3 matrix such that A+AT=O. If A[

−1

]=[

],A2[

−1

]=[

−3

−24

] and det(adj(2‌adj(A+I)))=(2)α⋅(3)β⋅(11)γ,α,β,γ are nonnegative integers, then α+β+γ is equal to ____

[22 Jan 2026 Shift 1]

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