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  • Explain Solution for RD Sharma Maths Class 12 Chapter 6 Adjoint and inverse of a Matrix Exercise very short answer type Question 13 maths textbook solution

Explain Solution for RD Sharma Maths Class 12 Chapter 6 Adjoint and inverse of a Matrix Exercise very short answer type Question 13 maths textbook solution

Answers (1)

VSQ : 13

Answer : null matrix 

Given : A is a square matrix 

Hint : use the formula of adj\left ( A^{T} \right ) & adj\left ( A \right )^{T}

Solution : We know that

\begin{aligned} &\operatorname{adj}\left(A^{T}\right)=\left|A^{T}\right|\left(A^{T}\right)^{-1}\\ &\operatorname{adj}(A)^{T}=\left(|A| A^{-1}\right)^{T}\\ &\text { Now, we have }\\ &\operatorname{adj}\left(A^{T}\right)-\operatorname{adj}(A)^{T}\\ &=\left|A^{T}\right|\left(A^{T}\right)^{-1}-\left[|A| A^{-1}\right]^{T}\\ &=0 \quad \end{aligned}                           \left[\because A^{\top} \cdot A^{-\top}=1\right]

 

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