Evaluate :

$\begin{bmatrix$}[r] 2cos60° & -2sin30° \ -tan 45° & cos0° \end{bmatrix}\begin{bmatrix}[r] cot 45° & cosec 30° \ sec60° & sin 90° \end{bmatrix}

Given,

$\Rightarrow \begin{bmatrix$}[r] 2cos60° & -2sin30° \ -tan 45° & cos0° \end{bmatrix}\begin{bmatrix}[r] cot 45° & cosec 30° \ sec60° & sin 90° \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] 2 \times \dfrac{1}{2} & -2 \times \dfrac{1}{2} \ -1 & 1 \end{bmatrix}\begin{bmatrix}[r] 1 & 2 \ 2 & 1 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] 1 & -1 \ -1 & 1 \end{bmatrix}\begin{bmatrix}[r] 1 & 2 \ 2 & 1 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] 1 \times 1 + (-1) \times 2 & 1 \times 2 + (-1) \times 1 \ -1 \times 1 + 1 \times 2 & -1 \times 2 + 1 \times 1 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] 1 - 2 & 2 - 1 \ -1 + 2 & -2 + 1 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] -1 & 1 \ 1 & -1 \end{bmatrix}.

Hence, $\begin{bmatrix$}[r] 2cos60° & -2sin30° \ -tan 45° & cos0° \end{bmatrix}\begin{bmatrix}[r] cot 45° & cosec 30° \ sec60° & sin 90° \end{bmatrix} = \begin{bmatrix}[r] -1 & 1 \ 1 & -1 \end{bmatrix}.