MathsJEE Main 8 Apr 2026, Shift 2·Q4·MCQ·Moderate

Matrices & Determinants · Adjoint and determinant properties

Let

A = \begin{bmatrix} \alpha & 1 & 2\\ 2 & 3 & 0\\ 0 & 4 & 5\end{bmatrix} \quad\text{and}\quad B = \begin{bmatrix} 1 & 0 & 0\\ 0 & -5\alpha & 0\\ 0 & 4\alpha & -2\alpha\end{bmatrix} + \operatorname{adj}(A).

If

\det(B) = 66

, then

\det(\operatorname{adj}(A))

equals:

(1)289
(2)361
(3)441
(4)529

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