If A, B find AB and BA if possible

Question

Question:

If A = $\left[ \begin{matrix} 3 & 0 \ -1 & 2 \ \end{matrix} ight]$, B = $\left[ \begin{matrix} 6 \ 5 \ \end{matrix} ight]$, find

(i) AB

(ii) BA (if possible)

Accepted Answer

Solution:

(i) AB

= $\left[ \begin{matrix} 3 & 0 \ -1 & 2 \ \end{matrix} ight] imes \left[ \begin{matrix} 6 \ 5 \ \end{matrix} ight]$

= $\left[ \begin{matrix} 3 imes 6+0 imes 5 \ \left( -1 ight) imes 6+2 imes 5 \ \end{matrix} ight]$

= $\left[ \begin{matrix} 18+0 \ -6+10 \ \end{matrix} ight]$

= $\left[ \begin{matrix} 18 \ 4 \ \end{matrix} ight]$

So, AB = $\left[ \begin{matrix} 18 \ 4 \ \end{matrix} ight]$

(ii) BA

BA is not possible as it is not conformable for multiplication (number of columns of B is not equal to number of rows of A).