For a 3 × 3 matrix M, let trace(M) denote the sum of all the diagonal elements of M. Let A be a 3 × 3 matrix such that |A|=1/2 and trace(A)=3. If B=adj(adj(2 A)), then the value of |B|+trace(B) equals:

Matrices and Determinants: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q26

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumMatrices and Determinants245× since 2002

For a

3 \times 3

matrix

M

, let

\text{trace}(M)

denote the sum of all the diagonal elements of

M

. Let

A

be a

3 \times 3

matrix such that

|A|=\frac{1}{2}

and

\text{trace}(A)=3

. If

B=\text{adj}(\text{adj}(2 A))

, then the value of

|B|+\text{trace}(B)

equals: