Given $A = \begin{bmatrix} \sqrt{3} & 1 & -1 \\ 2 & 3 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & \sqrt{5} & 1 \\ -2 & 3 & \frac{1}{2} \end{bmatrix}$, find $A + B$.

$\begin{bmatrix} 2 + \sqrt{3} & 1 + \sqrt{5} & 0 \\ 0 & 6 & 1/2 \end{bmatrix}$

The correct answer is Option (2) → $\begin{bmatrix} 2 + \sqrt{3} & 1 + \sqrt{5} & 0 \\ 0 & 6 & 1/2 \end{bmatrix}$ ##

Since $A, B$ are of the same order $2 \times 3$. Therefore, addition of $A$ and $B$ is defined and is given by

$A + B = \begin{bmatrix} 2 + \sqrt{3} & 1 + \sqrt{5} & 1 - 1 \\ 2 - 2 & 3 + 3 & 0 + \frac{1}{2} \end{bmatrix} = \begin{bmatrix} 2 + \sqrt{3} & 1 + \sqrt{5} & 0 \\ 0 & 6 & \frac{1}{2} \end{bmatrix}$