Which Clifford Algebras Admit Multiplicative Inverses?

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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?
 
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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" "
 
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