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Explain solution RD Sharma class 12 Chapter 6 Adjoint and Inverse of a Matrix exercise Fill in the blanks question 23

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Answer   \rightarrow 3\times 3

Hint   \rightarrow(\operatorname{adj} A)=|A|^{n-1}

Given  \rightarrow|(\operatorname{adj} A)|=|A|^{2}

Explanation  \rightarrow \text { adj } A=|A| A^{-1}

                |\operatorname{adj} A|=|A|^{n-1}

                |A|^{2}=|A|^{n-1}                            … [ given |(\operatorname{adj} A)|=|A|^{2} ]

                \begin{aligned} &n-1=2 \\ &n=3 \end{aligned}

               

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