To reflect the given matrix over the x-axis, you have to multiply both matrices:
[tex]\begin{bmatrix}{1} & {0} \\ {0} & {-1}\end{bmatrix}\cdot\begin{bmatrix}{7} \\ {-12}\end{bmatrix}[/tex]
Multiply each term of the first row of the first matrix with the corresponding terms of the column of the second matrix and add the results:
Repeat the process for the second row of the first matrix
The resulting matrix is:
[tex]\begin{bmatrix}{1} & {0} \\ {0} & {-1}\end{bmatrix}\cdot\begin{bmatrix}{7} \\ {-12}\end{bmatrix}=\begin{bmatrix}{(1\cdot7)+(0\cdot-12)} \\ {\square}(0\cdot7)+(-1\cdot-12)\end{bmatrix}=\begin{bmatrix}{7} \\ {12}\end{bmatrix}[/tex]
The correct option is option D.
