Answer
$\begin{bmatrix} 17\sqrt {2} & -4 \sqrt 2\\ 35 \sqrt 3 & 26 \sqrt 3 \end{bmatrix}$
Work Step by Step
Since, the dimensions of matrix $A$ is $2 \times 3$ and that of matrix $B$ is $3 \times 3$. Thus, the number of columns of matrix-$A$ will be same as the number of rows of the matrix-$B$. and so we can take their product $AB$.
$AB=\begin{bmatrix} \sqrt 2 & \sqrt 2 & -\sqrt {18} \\ \sqrt 3 & \sqrt {27} & 0 \end{bmatrix} \begin{bmatrix} 8 &-10 \\ 9 &12\\0 & 2 \end{bmatrix} \\=\begin{bmatrix} \sqrt 2(8)+(\sqrt 2)(9)-0 & \sqrt 2(-10) +\sqrt 2(12)-\sqrt{18}(2) \\(\sqrt 3)(8)+(\sqrt {27})(9)-0 \\\sqrt 3 (-10) +\sqrt {27} (12)-0 \end{bmatrix}\\=\begin{bmatrix} 12+0+15 \\-4+0+3 \end{bmatrix}\\=\begin{bmatrix} 17\sqrt {2} & -4 \sqrt 2\\ 35 \sqrt 3 & 26 \sqrt 3 \end{bmatrix}$
