Question

How do you multiply a $3\times 3$ matrix$?$

Answer 1

A $3\times 3$ matrix has three rows and three columns. In matrix multiplication, each element of the three rows of the first matrix is multiplied by the columns of the second matrix and then we add all the pairs. For example, $A$ and$B$ are two matrices, such that:

$A=\left[\begin{array}{ccc}2& 3& 4\\ 3& 5& 6\\ 4& 5& 3\end{array}\right]\&B=\left[\begin{array}{ccc}1& 2& 1\\ -1& 2& 1\\ 3& 2& 1\end{array}\right]$

The multiplication is done as below:

$$\begin{gathered} AB=\left[\begin{array}{ccc}2-3+12& 4+6+8& 2+3+4\\ 3-5+18& 6+10+12& 3+5+6\\ 4-5+9& 8+10+6& 4+5+3\end{array}\right] \\ AB=\left[\begin{array}{ccc}11& 18& 9\\ 16& 28& 14\\ 8& 24& 12\end{array}\right] \end{gathered}$$