Let $F$ be a field of characteristic $\neq 2$. Suppose $(A,\sigma)$ is central simple algebra over a field $F$ with an orthogonal involution. Assume $(A,\sigma)$ is non-split. How to show that every left ideal is generated by a symmetric element? It appears as an exercise in 'The Book of involution', Ch.I. Can somebody provide hint for doing this?
Thanks!