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  • Provide Solution for RD Sharma Class 12 Chapter 6 Adjoint and Inverse of a Matrix Exercise 6.1 Question 7 subquestion (i)

Provide Solution for RD Sharma Class 12 Chapter 6 Adjoint and Inverse of a Matrix Exercise 6.1 Question 7 subquestion (i)

Answers (1)

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Answer:

A^{-1}=\left[\begin{array}{cc} \cos \theta &- \sin \theta \\ \sin \theta & \cos \theta \end{array}\right]

Hint:

Here, we use basic concept of inverse

Given:

  A=\left[\begin{array}{cc} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right]

Solution:

A^{-1}=\frac{1}{|A|} \times A d j(A)

Let’s find  \left | A \right |

|A|=\cos ^{2} \theta+\sin ^{2} \theta=1

So,

A^{-1}=\left[\begin{array}{cc} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right]

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