Evaluate :

$\begin{bmatrix$}[r] \text{2 sin 30°} & \text{-2 cos 60°} \ \text{-cot 45°} & \text{-sin 90°} \end{bmatrix}\begin{bmatrix}[r] \text{tan 45°} & \text{sec 60°} \ \text{cosec 30°} & \text{cos 0°} \end{bmatrix}

Solving,

$\Rightarrow \begin{bmatrix$}[r] \text{2 sin 30°} & \text{-2 cos 60°} \ \text{-cot 45°} & \text{-sin 90°} \end{bmatrix}\begin{bmatrix}[r] \text{tan 45°} & \text{sec 60°} \ \text{cosec 30°} & \text{cos 0°} \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 \ -3 & -3 \end{bmatrix}.

Hence, $\begin{bmatrix$}[r] \text{2 sin 30°} & \text{-2 cos 60°} \ \text{-cot 45°} & \text{-sin 90°} \end{bmatrix}\begin{bmatrix}[r] \text{tan 45°} & \text{sec 60°} \ \text{cosec 30°} & \text{cos 0°} \end{bmatrix} = \begin{bmatrix}[r] -1 & 1 \ -3 & -3 \end{bmatrix}.