Question

Can you multiply a $3x2$ and $2x2$ matrix?

Answer 1

Multiplication of matrix :

Let a matrix of order $m\times n$ and another matrix $n\times q$ then matrix can be multiply means number of column in first matrix is equal to the number of rows in second matrix then we can multiply the matrix.

Here we have to multiply $3\times 2$ matrix and $2\times 2$ matrix, which is possible and the resultant matrix will be $3\times 2$.

Let us understand with the help of an example.

Let $A=$$\left[\begin{array}{cc}0& 7\\ 3& 6\\ -2& 0\end{array}\right]$ and $B=$$\left[\begin{array}{cc}3& -4\\ 0& 12\end{array}\right]$

then, $AB=$$\left[\begin{array}{cc}0\times 3+0\times 7& -4\times 0+7\times 12\\ 3\times 3+6\times 0& -4\times 3+6\times 12\\ -2\times 3+(-2)\times 0& (-2)\times (-4)+12\times 0\end{array}\right]$
$=\left[\begin{array}{cc}0& 84\\ 9& 60\\ -6& 8\end{array}\right]$

Hence, In this way we can multiply the matrix.