Let a and A be a matrix of order 3×3 such that det (A)=-4 and A+I= 1 a 1 2 1 0 a 1 2, where I is the 3×3 identity. If det ((a+1) ((a-1)A))=2^(m)3ⁿ, m,n \0,1,2,,20 then m+n is equal to:

Matrices and Determinants: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q44

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

Let

a\in\mathbb{R}

and

A

be a matrix of order

3\times3

such that

\det(A)=-4

and

A+I=\begin{pmatrix}1 & a & 1\\2 & 1 & 0\\a & 1 & 2\end{pmatrix},

where

I

is the

3\times3

identity. If

\det\bigl((a+1)\adj((a-1)A)\bigr)=2^m3^n,\quad m,n\in\{0,1,2,\dots,20\},

then

m+n

is equal to: