Let α and β be complex numbers. Which of the following sets of matrices forms a group under matrix multiplication?
1
\(\left(\begin{array}{ll}\alpha & \beta \\ 0 & 0\end{array}\right)\)
2
\(\left(\begin{array}{ll}1 & \alpha \\ \beta & 1\end{array}\right)\) where αβ ≠ 1
3
\(\left(\begin{array}{ll}\alpha & \alpha^* \\ \beta & \beta^*\end{array}\right)\) where αβ* is real
4
\(\left(\begin{array}{cc}\alpha & \beta \\ -\beta^* & \alpha\end{array}\right)\) where |α|2 + |β|2 = 1