MathsJEE Main 6 Apr 2026, Shift 1·Q21·Numerical·Moderate

Matrices & Determinants · Properties of adjoint matrix

Let

A = \begin{bmatrix} -1 & 1 & -1\\ 1 & 0 & 1\\ 0 & 0 & 1\end{bmatrix}

satisfy

A^2 + \alpha(\operatorname{adj}(\operatorname{adj}(A))) + \beta(\operatorname{adj}(A)(\operatorname{adj}(\operatorname{adj}(A)))) = \begin{bmatrix} 2 & -2 & 2\\ -2 & 0 & -1\\ 0 & 0 & -1\end{bmatrix}

for Some

\alpha, \beta \in \mathbb{R}

. Then

(\alpha - \beta)^2

is equal to .

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