Here is the problem:
Let be a field and a quadratic space with an anisotropic form not representing (i.e. for all ). Show that if and are not both zero, then is an invertible element in the Clifford algebra .
I'm not really sure how to start this problem. I don't fully understand Clifford algebras, so I don't even really know what invertible elements even look like. I understand the definition - , where I is the ideal generated by - but I don't understand the resulting algebra (except when is a binary or nonzero unary form).
Any help is appreciated.