Question

Let A be a 3 × 3 square matrix, such that A (adj A) = 2 I, where I is the identity matrix. Write the value of |adj A|.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{know}\mathrm{that}\mathrm{for}\mathrm{a}\mathrm{matix}A\mathit{}\mathrm{of}\mathrm{order}\mathit{}n\mathit{,}\mathit{}A.\left(adjA\right)=\left|A\right|I_n,\mathrm{where}I\mathrm{is}\mathrm{the}\mathrm{identity}\mathrm{matrix}. \\ \mathrm{Given}:A.\left(adjA\right)=2I \\ \Rightarrow \left|A\right|I=2I \\ \Rightarrow \left|A\right|=2 \\ \mathrm{Now}, \\ \left|adjA\right|={\left|A\right|}^{n-1} \\ \Rightarrow \left|adjA\right|=2^2=4 \end{gathered}$$