Irredundant and Almost Irredundant Sets in \(\mathbb{M}_2\)(\(\mathbb{C}\))

We consider irredundant and almost irredundant subsets in the *-algebra \(\mathbb{M}_2\)(\(\mathbb{C}\)) of all 2 X 2 matrices with coefficients in \(\mathbb{C}\). We prove that the largest size of an irredundant subset is two, and that \(\mathbb{M}_2\)(\(\mathbb{C}\)) has an infinite almost irredundant subset.