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