Let |A|=6, where A is a 3×3 matrix. If |adj(3 adj(A² (2A)))|=2^(m)·3ⁿ, m,n, then m+n is equal to _ _ _.

Matrices and Determinants: JEE Main 2026 Mathematics question

JEE Main 2026 · 23 Jan, Morning shift · Q22

JEE Main 202623 Jan, Morning shiftMathematicsMediumMatrices and Determinants245× since 2002

Let

|A|=6

, where A is a

3\times3

matrix. If

|\mathrm{adj}(3\,\mathrm{adj}(A^2\cdot\mathrm{adj}(2A)))|=2^m\cdot3^n

m,n\in\mathbb{N}

, then

m+n

is equal to ______.

Your answerType your answer. Integers and decimals are accepted.