Question

If \(A = \left[ \begin{array}{cc} 1 & \cot \frac{\theta}{2} \\ -\cot \frac{\theta}{2} & 1 \end{array} \right]\) then \(A^{-1} =\)

• A. \(\text{cosec}^2 \frac{\theta}{2} A^{\text{T}}\)
• B. \(\frac{-\sin^2 \theta}{2} A^{\text{T}}\)
• C. \(\left( \frac{1+\cos \theta}{2} \right) A^{\text{T}}\)
• D. \(\left( \frac{1-\cos \theta}{2} \right) A^{\text{T}}\)

Hint:

Whenever a matrix inverse option is given in terms of \(A^T\), first compute the determinant and check whether the adjoint resembles the transpose.

Answer 1

The Correct Option is D