Answer:
The entry on the second row and second column of the product matrix is
.
Explanation:
Let's define as A and B the given matrixes:
![A = \left[\begin{array}{cc}1&2\\3&4\end{array}\right]](https://img.qammunity.org/2020/formulas/mathematics/college/bk14gxi5wk6ob11bsn6wfoir57bqcl8cg0.png)
![B = \left[\begin{array}{cc}9&6\\5&7\end{array}\right]](https://img.qammunity.org/2020/formulas/mathematics/college/fruaam8u9err9tqrs22sdfmg6mvcdt0rsh.png)
The product matrix C entry in the first row and first column
or
can be computer multiplying first row of A by first column of B (see example attached).
The product matrix C entry in the first row and second column
or
can be computer multiplying first row of A by second column of B.
The product matrix C entry in the second row and first column
or
can be computer multiplying second row of A by first column of B.
The product matrix C entry in the second row and second column
or
can be computer multiplying second row of A by second column of B.
Then, let's compute
by doing the dot product between [3 4] and [6 7]...
![c_(22) = [3 4] . [6 7] = 3*4 + 4*7 = 12 + 28 = 40](https://img.qammunity.org/2020/formulas/mathematics/college/wo0lhtrcctm7qw56yoyl028al0avh4l06d.png)