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  • Explain solution for RD Sharma maths Class 12 Chapter 5 Determinants Exercise VSQ Question 39 maths textbook solution.

Explain solution for RD Sharma maths Class 12 Chapter 5 Determinants Exercise VSQ Question 39 maths textbook solution.

Answers (1)

Answer:2

Hint: Here we use basic concept of determinant of matrix

Given: |A|=2

A is 2 \times 2 matrix so, n=2

Solution :

|\operatorname{adj} A|

\rightarrow We know that

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

So, \operatorname{adj}(A)=k A^{-1}

\rightarrow Let's take determinate both sides

\begin{aligned} &|\operatorname{adj}(A)|=\left|k A^{-1}\right| \\ &|\operatorname{adj}(A)|=k^{n}\left|A^{-1}\right| \\ &\rightarrow \text { Here } \mathrm{k}=|A|, \mathrm{n} \text { is } 2 \end{aligned}

Hence,  |\operatorname{adj}(A)|=|A|^{n}\left|A^{-1}\right|

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

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