Let adj \textrm{ } \left(\right. A \left.\right) = \left[\right. \textrm{ }\textrm{ } 2 & 1 & 3 \\ 3 & 1 & 2 \\ 2 & 2 & - 1 \textrm{ }\textrm{ } \left]\right. then the value of det(adj(adj 2A)) is

Engineering

Mathematics

Transpose and Adjoint of a Matrix

Question

Let $adj (A) = [\begin{matrix} 2 & 1 & 3 \\ 3 & 1 & 2 \\ 2 & 2 & - 1 \end{matrix}]$ then the value of det(adj(adj 2A)) is

(18)⁴

12⁴

(24)⁴

6⁴

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| adj A | = | A |² = 9, and |adj adj(2A)| = |(2A)|⁴ = (2³ |A|)⁴

2¹² · |A|⁴ = 2¹² · 9² = 2⁴².