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  • Explain solution RD Sharma class 12 Chapter 6 Adjoint and Inverse of a Matrix exercise Fill in the blanks question 15

Explain solution RD Sharma class 12 Chapter 6 Adjoint and Inverse of a Matrix exercise Fill in the blanks question 15

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Answer  \rightarrow k^{2} I

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

Given  \rightarrow k is a scalar and I  is a unit matrix of order  3

Explanation  \rightarrow \operatorname{adj}(k I)=k^{n-1}(a d j I)

                \begin{aligned} &\operatorname{adj}(k I)=k^{3-1} a d j(I) \\\\ &=k^{2} \cdot I \end{aligned}

Hence,  \operatorname{adj}(k I)=k^{2} \cdot I

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