### Home > PC > Chapter 12 > Lesson 12.2.2 > Problem12-51

12-51.

Earlier we found the matrix associated with the composition of rotating $90°$ counterclockwise and then reflecting across the $x$-axis. Now find the matrix associated with reflecting across the $x$-axis and then rotating $90°$.

From problem 12-45:
$A =$ matrix associated with $90º$ counterclockwise rotation
$B =$ martix associated with reflecting across the $x$-axis

$A = \left[ \begin{array} { c c } { 0 } & { 1 } \\ { - 1 } & { 0 } \end{array} \right] \quad B = \left[ \begin{array} { c c } { 1 } & { 0 } \\ { 0 } & { - 1 } \end{array} \right]$

Multiply $A$ and $B$ in the opposite order you did in problem 12-45. That is, find $BA$.