Which Clifford Algebras Admit Multiplicative Inverses?

[mnb96]

Hello,
Let's assume we have a Clifford algebra of one of the following two kinds: $$\mathcal{C}\ell_{n,0}$$ or $$\mathcal{C}\ell_{0,n}$$.

Is it possible to say which algebras will admit a multiplicative inverse for each multivector element?

 

[arkajad]

$$Cl_{0,1}=\bf{C}$$
$$Cl_{0,2}=\bf{H}$$

See the table on p. 11 in Atiyah, Bott, Shapiro "http://www.dleex.com/read/7878" "