MathsJEE Main 21 Jan 2026, Shift 1·Q24·Numerical·Moderate

Matrices & Determinants · Adjoint and determinant properties

For some

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

, let

A = \begin{bmatrix} \alpha & 2\\ 1 & 2\end{bmatrix} \quad\text{and}\quad B = \begin{bmatrix} 1 & 1\\ 1 & \beta\end{bmatrix}

be such that

A^2 - 4A + 2I = B^2 - 3B + I = O

. Then

(\det(\operatorname{adj}(A^3 - B^3)))^2

is equal to .

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