How do I use matrix multiplication to find the reflection of (-1,2) about the x axis, y axis and the line y=x?
2026-03-29 17:23:09.1774804989
Matrix Transformation - Using matrix multiplication
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Each one of those is a linear transformation, so can be represented by matrix multiplication. Let's say the first one, reflection about the $x$-axis. Say, it is represented by some matrix $A$. Then, $$ A \pmatrix{1\\0} = \pmatrix{1\\0} \text{ and } A \pmatrix{0\\1} = \pmatrix{0\\-1}, $$ so $$ A \pmatrix{1 & 0\\0 & 1} = \pmatrix{1 & 0\\0 & -1} $$ Do you now know what $A$ is? What happens when you compute $$ A \pmatrix{-1\\2}? $$
Can you do the others the same way?