Which of the following sets are compact?
a. The closed unit ball centred at $0$ and of radius $1$ of $\ell_1$ (with the metric $d_1({a_i},{b_i}) = \sum_{i=1}^\infty|a_i - b_i |$).
b. The set of all unitary matrices in $M_2(\Bbb C)$.
c. The set of all matrices in $M_2(\Bbb C)$ with determinant equal to unity.
i know that (b) is true. and (c) is false as it is not bounded. but can't find anything for (a). thank you.