Find inverse of $[\begin{matrix} csc θ & - cot θ cot θ & csc θ \end{matrix}]$

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Solution

$A^{- 1} = \frac{A d j A}{D e t A} A d j A = [\begin{matrix} csc θ & cot θ - cot θ & csc θ \end{matrix}] D e t A = {csc}^{2} θ + {cot}^{2} θ A^{- 1} = \frac{1}{{csc}^{2} θ + {cot}^{2} θ} [\begin{matrix} csc θ & - cot θ cot θ & csc θ \end{matrix}]$

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