Let H be the subset of $M_2(\mathbb{R})$ consisting of all matrices of the form
$H^* = \left \{ \begin{pmatrix} a &-b \\ b&a \end{pmatrix} : a,b\in\mathbb{R} , a\neq 0 \; \text{or} \; b \neq 0\right\}$
Is (H*, .) a group under multiplication?
I said no because since $b \neq 0$, the identity matrix can't exist. But my prof briefly said "either a or b can't be 0, not a and b"
Am I right or his wrong?