\(\mathbf { M } _ { 2 } = \left( \begin{array} { r r } 1 & 0 0 & - 1 \end{array} \right)\)
Find the equation of the mirror line of the reflection R represented by the matrix \(\mathbf { M } _ { 3 } = \mathbf { M } _ { 1 } \mathbf { M } _ { 2 }\).
It is claimed that the reflection represented by the matrix \(\mathbf { M } _ { 4 } = \mathbf { M } _ { 2 } \mathbf { M } _ { 1 }\) has the same mirror line as R . Explain whether or not this claim is correct.