### Home > PC > Chapter 12 > Lesson 12.1.1 > Problem12-6

12-6.

Let $A = \begin{bmatrix} { 1 } & { 2 } \\ { 3 } & { 4 } \end{bmatrix}$ and let $B = \begin{bmatrix} { - 1 } & { 0 } \\ { 2 } & { 1 } \end{bmatrix}$.

1. Find $AB$ and $BA$.

When multiplying matrices, multiply the rows of the first matrix by the columns of the second matrix.

$AB=\begin{bmatrix}1(-1)+2(2)&1(0)+2(1)\\3(-1)+4(2)&3(0)+4(1)\end{bmatrix}$

Now simplify and then calculate $BA$ on your own.

2. What can you conclude about multiplying square matrices?

Does $AB = BA$?