Question

If A=
`\left[\begin{array}{ccc}-4&-3&5\\-5&-4&-2\\-1&-2&-4\end{array}\right]` and B=
`\left[\begin{array}{ccc}3&-4&-1\\-5&-5&1\\-1&-3&2\end{array}\right]`, find AB.

Answer 1

It's not C because

`(AB)_(1,1)=A_(1,c)B_(r,1)=\begin{bmatrix}-4&-3&5\end{bmatrix}\begin{bmatrix}3\\-5\\-1\end{bmatrix}=-2`

where
`(AB)_(1,1)` denotes the element of
`AB` in row 1, column 1,
`A_(1,c)` denotes the first row of
`A`, and
`B_(r,1)` denotes the first column of
`B`.

It's not A because

`(AB)_(1,2)=A_(1,c)B_(r,2)=\begin{bmatrix}-4&-3&5\end{bmatrix}\begin{bmatrix}-4\\-5\\-3\end{bmatrix}=16`

It's not D because

`(AB)_(2,2)=A_(2,c)B_(r,2)=\begin{bmatrix}-5&-4&-2\end{bmatrix}\begin{bmatrix}-4\\-5\\-3\end{bmatrix}=46`

So B must be the correct answer (and it is).