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  • Please Solve RD Sharma Class 12 Chapter 6 Adjoint and Inverese of Matrices Exercise 6.1 Question 35 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 6 Adjoint and Inverese of Matrices Exercise 6.1 Question 35 Maths Textbook Solution.

Answers (1)

Answer:

|A \times \operatorname{Adj}(A)|=|A|^{n}

Hint:

Here, we use basic concept of determinant and inverse of matrix

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

Given:

A is square matrix

Solution:

\begin{aligned} &|A \times \operatorname{Adj}(A)|=|A|^{n} \\ &L H S \\ &|A \times \operatorname{Adj}(A)| \\ &=|A| \times|A|^{n-1} \end{aligned}                                           \left[A d j(A)=|A|^{n-1}\right]
\begin{aligned} &=|A|^{n+1-1} \\ &=|A|^{n} \\ &=R H S \end{aligned}

 

 

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