Originally Posted by

**redsoxfan325** Here is the problem:

Let $\displaystyle F$ be a field and $\displaystyle V$ a quadratic space with an anisotropic form $\displaystyle q$ not representing $\displaystyle 1$. Show that if $\displaystyle a\in F$ and $\displaystyle v\in V$ are not both zero, then $\displaystyle a+v$ is an invertible element in the Clifford algebra $\displaystyle C(V,q)$.

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 - $\displaystyle T(V)/I$, where I is the ideal generated by $\displaystyle v\otimes v-q(v)$ - but I don't understand the resulting algebra (except when $\displaystyle q$ is a binary or nonzero unary form).

Any help is appreciated.