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Provide Solutio for RD Sharma Class 12 Chapter 6 Adjoint and Inverse Matrix Exercise Fill in the blanks Question 14

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Answer  \rightarrow 25

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

Given  \rightarrow A is a square matrix of order 3  and  B=|A| A^{-1} and  |A|=5

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

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

                B=\operatorname{adj} A=|A| A^{-1}                   …(given)

                \begin{aligned} &|B|=|\operatorname{adj} A| \\\\ &=|A|^{n-1} \\\\ &=(5)^{2}=25 \end{aligned}

Hence, \left | B \right |=25

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