Matrix Equation and Determinant (Jee Mains) | ExamDuo
Determinants
Hard
Matrix Equation and Determinant
Let A be a 3 × 3 matrix such that A + AT = O. If and det(adj(2adj (A + I))) = (2)α.(3)β.(11)γ, α, β, γ are non-negative integers, then α + β + γ is equal to ______.
![A\left[ {\begin{array}{*{20}{c}} 1\\[0.9em] { - 1}\\[0.9em] 0 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 3\\[0.9em] 3\\[0.9em] 2 \end{array}} \right],{A^2}\left[ {\begin{array}{*{20}{c}} 1\\[0.9em] { - 1}\\[0.9em] 0 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} { - 3}\\[0.9em] {19}\\[0.9em] { - 24} \end{array}} \right]](https://d2lbh14zkcqlst.cloudfront.net/content_data/content_images/1771490941554468814.png)
and det(adj(2adj (A + I))) = (2)α.(3)β.(11)γ, α, β, γ are non-negative integers, then α + β + γ is equal to ______.