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Please Solve RD Sharma Class 12 Chapter 6 Adjoint and Inverse of a Matrix  Exercise fill in the blaks Question 10 Maths Textbook Solution.

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Answer   \rightarrow 256

Hint   \rightarrow|\operatorname{adj}(\operatorname{adj} A)|=|A|^{(n-1)^{2}}

Given  \rightarrow A is an invertible matrix of order 3 and \left | A \right |=4

Explanation   \rightarrow A(\operatorname{adj} A)=|A| I

                |A(\operatorname{adjA})|=\| A|I|

                |A||\operatorname{adj} A|=|A|^{n}                 \left[|| A|I|=|A|^{n} \quad \text { and }|A B|=|A||B|\right] 

                \begin{aligned} &|\operatorname{adj} A|=|A|^{n-1} \\\\ &|\operatorname{adj}(\operatorname{adj} A)|=|\operatorname{adj} A|^{n-1} \end{aligned}

                \begin{aligned} &\left.=| A\right|^{n-1)(n-1)} \\\\ &=|A|^{(n-1)^{2}} \\ \\&=(4)^{(3-1)^{2}} \\\\ &=(4)^{4} \\\\ &=256 \end{aligned}



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