Determine the type of transformation represented by the following matrix. \( \left[\begin{array}{cc}1 & 0 \\ 0 & -1\end{array}\right] \) Reflection with respect to the Select

1. The given matrix is \[ A = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}. \] 2. Notice that when this matrix acts on a vector \[ \begin{pmatrix} x \\ y \end{pmatrix}, \] the result is \[ A \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 1 \cdot x + 0 \cdot y \\ 0 \cdot x + (-1) \cdot y \end{pmatrix} = \begin{pmatrix} x \\ -y \end{pmatrix}. \] 3. This operation leaves the \(x\)-coordinate unchanged while reversing the \(y\)-coordinate. Such a transformation reflects every point across the \(x\)-axis. 4. Therefore, the matrix \( A \) represents a reflection with respect to the \(x\)-axis.