If $A=\begin{bmatrix}1 & \sqrt{3} & 0\\-\sqrt{3} & 1& 0\\0 & 0 & 2\end{bmatrix} $ and $B=\begin{bmatrix} \sqrt{3} & 1 & 0\\-1 & \sqrt{3} & 0\\0 & 0 & 2\end{bmatrix} $ then AB is equal to :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $\begin{bmatrix}0& 4 & 0\\-4 & 0 & 0\\0 & 0 & 4\end{bmatrix}$
$AB=\begin{bmatrix}1 & \sqrt{3} & 0\\-\sqrt{3} & 1& 0\\0 & 0 & 2\end{bmatrix}\begin{bmatrix} \sqrt{3} & 1 & 0\\-1 & \sqrt{3} & 0\\0 & 0 & 2\end{bmatrix}$
$=\begin{bmatrix}0& 4 & 0\\-4 & 0 & 0\\0 & 0 & 4\end{bmatrix}$