Answer:
Option: B is the correct answer.
\(B.\ \left[\begin{array}{ccc}6&24\\3.4&13\end{array}\right]\)
Step-by-step explanation:
We are given two matrices A and B as follows:
\(A=\left[\begin{array}{ccc}3&0\\2&-1\end{array}\right]\)
and
\(B=\left[\begin{array}{ccc}2&8\\0.6&3\end{array}\right]\)
We know that the multiplication of two matrices of the type:
\(A=\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]\)
and
\(B=\left[\begin{array}{ccc}a'&b'\\c'&d'\end{array}\right]\)
is given by:
\(AB=\left[\begin{array}{ccc}aa'+bc'&ab'+bd'\\ca'+dc'&cb'+dd'\end{array}\right]\)
Hence, here we have:
\(AB=\left[\begin{array}{ccc}3\times 2+0\times 0.6&3\times 8+0\times 3\\2\times 2+(-1)\times 0.6&2\times 8+(-1)\times 3\end{array}\right]\)
i.e.
\(AB=\left[\begin{array}{ccc}6+0&24+0\\4-0.6&16-3\end{array}\right]\)
i.e.
\(AB=\left[\begin{array}{ccc}6&24\\3.4&13\end{array}\right]\)
