Question:

Find AB if A $\displaystyle = \begin{pmatrix}z & y\\

x & w\\

v & u

\end{pmatrix} $ and B $\displaystyle = \begin{pmatrix}

a & b & c\\

d & e & f

\end{pmatrix} $

Solution:

A has a 3 X 2 matrix and B has a 2 X 3 matrix

thus AB has a 3 X 3 matrix

$\displaystyle

\begin{pmatrix}(za+yd) &(zb+ye) &(zc+yf) \\

(xa+wd) &(xb+we) &(xc+wf) \\

(va+ud)&(vb+ue) & (vc+uf)

\end{pmatrix} $

I would like to know if i am right