Answer
\[\left[ {\begin{array}{*{20}{c}}
{3 + 4\sqrt 3 }&{\sqrt {18} } \\
{2\sqrt {15} + 12\sqrt 6 }&{ - 2\sqrt {30} }
\end{array}} \right]\]
Work Step by Step
\[\begin{gathered}
AB = \left[ {\begin{array}{*{20}{c}}
{\sqrt 3 }&1 \\
{2\sqrt 5 }&{3\sqrt 2 }
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
{\sqrt 3 }&{ - \sqrt 6 } \\
{4\sqrt 3 }&0
\end{array}} \right] \hfill \\
{\text{Multiply elements of each row of each column of }}A{\text{ by }} \hfill \\
{\text{elements of each column of }}B \hfill \\
AB = \left[ {\begin{array}{*{20}{c}}
{\left( {\sqrt 3 } \right)\left( {\sqrt 3 } \right) + \left( 1 \right)\left( {4\sqrt 3 } \right)}&{\left( {\sqrt 3 } \right)\left( { - \sqrt 6 } \right) + \left( 1 \right)\left( 0 \right)} \\
{\left( {2\sqrt 5 } \right)\left( {\sqrt 3 } \right) + \left( {3\sqrt 2 } \right)\left( {4\sqrt 3 } \right)}&{\left( {2\sqrt 5 } \right)\left( { - \sqrt 6 } \right) + \left( {3\sqrt 2 } \right)\left( 0 \right)}
\end{array}} \right] \hfill \\
{\text{Simplify}} \hfill \\
AB = \left[ {\begin{array}{*{20}{c}}
{3 + 4\sqrt 3 }&{\sqrt {18} } \\
{2\sqrt {15} + 12\sqrt 6 }&{ - 2\sqrt {30} }
\end{array}} \right] \hfill \\
\end{gathered} \]
