<u>Answer:</u>
A = \begin{pmatrix}-1 & 0 \\0 & -1\end{pmatrix}
<u>Step-by-step explanation:</u>
Let, there be a point (x , y) in R2
After reflection on Y axis, it will be ( -x , y) and thereafter if we reflect the image over X -axis , it will be (-x , -y)
So,
we need to find out a matrix
[tex]\begin{pmatrix}a & b \\c & d\end{pmatrix}[tex]
such that,
(x , y)
[tex]\begin{pmatrix}a & b \\c & d\end{pmatrix}[tex] = (-x. -y)
So, we have the following set of equations.
ax + cy = -x ------------(1)
bx + dy= -y-----------(2)
We can get the solution (by inspection) as,
[tex]\begin{pmatrix}a & b \\c & d\end{pmatrix}[tex]
= [tex]\begin{pmatrix}-1 & 0 \\0 & -1\end{pmatrix}[tex]
So, the matrix is,
A = \begin{pmatrix}-1 & 0 \\0 & -1\end{pmatrix} (answer)
