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

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

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Answer    \rightarrow \left ( 11 \right )^{4}=14,641

Hint \rightarrow   Determinant of cofactors of elements of  A is equal to the determinant of adjoint A

Given  \rightarrow A is a matrix of order 3 and  \left | A \right |=11

Explanation    \begin{aligned} &\rightarrow|A|=A(\operatorname{adj} A) \\\\ &|A|=A(C)^{T} \end{aligned}

               

Where C represents the cofactor of elements of  A

                \begin{aligned} &|C|^{T}|A|=\operatorname{det}(|A| I) \\\\ &\operatorname{det}\left(C^{T}\right)=|A|^{3}=|A|^{3-1} \\ \\&\operatorname{det}\left(C^{T}\right)=|A|^{2} \\ & \end{aligned}

                \! \! \! \! \! \! \! |B|=|A|^{2} \\\\ =(11)^{2} \\\\ =121

Hence,      \left | B \right |^{2}=\left ( 121 \right )^{2}

                =14641

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