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Please Solve RD Sharma Class 12 Chapter 6 Adjoint and Inverse of a Matrix  Exercise fill in the blaks Question 17 Maths Textbook Solution.

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Answer  \rightarrow|A| A

Given  \rightarrow is a non-singular matrix of order 3

Explanation   \rightarrow|A|=A . \operatorname{adj} A                                            …(i)

                (\operatorname{adj} A)^{-1}=\frac{A}{|A|}

                (\operatorname{adj} A)^{-1}=\frac{\operatorname{adj}(\operatorname{adj} A)}{\operatorname{det}(\operatorname{adj} A)}                      [A=a d j(a d j(A)) \text { and } \operatorname{det}(\operatorname{adj} A)=(\operatorname{det} \operatorname{det} A)^{n-1} ]

                \operatorname{adj}(\operatorname{adj} A)=(\operatorname{adj} A)^{-1} \operatorname{det}(\operatorname{adj} A)

                                     =(\operatorname{det} A)^{n-1} \times \frac{A}{\operatorname{det}(A)}                            [\operatorname{det}(\operatorname{adj} A)=(\operatorname{det} \operatorname{det} A)^{n-1}]               

                                     =(\operatorname{det} A)^{n-2} A

Now, n= 3

                \begin{aligned} &\operatorname{adj}(\operatorname{adj} A)=(\operatorname{det} A) A \\\\ &=|A| A \end{aligned}


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