Let A be a 3 × 3 matrix such that A^(T) 1 0 1 = 5 2 2, A^(T) 0 0 1 = 3 1 1, A 1 0 1 = 3 4 4 and A 0 0 1 = 1 3 1. If det (A) = 1, then det (adj(A² + A)) is equal to:

Matrices and Determinants: JEE Main 2026 Mathematics question

JEE Main 2026 · 5 Apr, Morning shift · Q3

JEE Main 20265 Apr, Morning shiftMathematicsMediumMatrices and Determinants245× since 2002

Let A be a

3 \times 3

matrix such that

A^T\begin{bmatrix}1\\0\\1\end{bmatrix}=\begin{bmatrix}5\\2\\2\end{bmatrix}

A^T\begin{bmatrix}0\\0\\1\end{bmatrix}=\begin{bmatrix}3\\1\\1\end{bmatrix}

A\begin{bmatrix}1\\0\\1\end{bmatrix}=\begin{bmatrix}3\\4\\4\end{bmatrix}

and

A\begin{bmatrix}0\\0\\1\end{bmatrix}=\begin{bmatrix}1\\3\\1\end{bmatrix}

. If

\det(A) = 1

, then

\det(\operatorname{adj}(A^2 + A))

is equal to:

JEE Main 2026 · 5 Apr, Morning shift · Q3

JEE Main 20265 Apr, Morning shiftMathematicsMediumMatrices and Determinants245× since 2002

Let A be a

3 \times 3

matrix such that

A^T\begin{bmatrix}1\\0\\1\end{bmatrix}=\begin{bmatrix}5\\2\\2\end{bmatrix}

A^T\begin{bmatrix}0\\0\\1\end{bmatrix}=\begin{bmatrix}3\\1\\1\end{bmatrix}

A\begin{bmatrix}1\\0\\1\end{bmatrix}=\begin{bmatrix}3\\4\\4\end{bmatrix}

and

A\begin{bmatrix}0\\0\\1\end{bmatrix}=\begin{bmatrix}1\\3\\1\end{bmatrix}

. If

\det(A) = 1

, then

\det(\operatorname{adj}(A^2 + A))

is equal to: