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Need solution for RD Sharma Maths Class 12 Chapter 6 Adjoint and Inverse of Matrix Excercise Fill in the Blanks Question 11

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Answer  \rightarrow 6^{4}=1296

Hint  \rightarrow In diagonal matrix all elements are zero except diagonal elements and its determinant is equal to product of diagonal elements.

Given    \rightarrow A=\operatorname{diag}(1,2,3)

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

                \begin{aligned} &|\operatorname{adj}(\operatorname{adj} A)|=|A|^{n-1)^{2}} \\\\ &=(6)^{(3-1)^{2}} \mid \\\\ &=(6)^{4} \\\\ &=1296 \end{aligned}

Hence, |\operatorname{adj}(\operatorname{adj} A)|=1296

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