If $r$ is a unit vector, the reflection with respect to the hyperplane of normal $r$ corresponds to the matrix $I-2rr^\top$ (known as a Householder matrix).
Now, let $r_1,r_2$ be two unit (column) vectors gathered in a matrix $R=[r_1,r_2]$. Is there an simple interpretation of the morphism associated to the matrix $I-2RR^\top$?
It's the mirror reflection on the plane $(r_1,r_2)$ :
$(I-2r\cdot r^\top)\cdot v = v-2\left( (v\cdot r_1)r_1+( v\cdot r_2)r_2 \right) = v-2v_p$ where $v_p$ is the projection of $v$ on plane $(r_1,r_2)$ .