Quick backstory. When I applied for this job about a year ago I had to interview with multiple people. It was between me an another gentleman, and it was about 50/50 with each interviewer voting on who they wanted. This woman wanted to hire the other person but I ended up getting the job.

I think due to this and her wanting to prove that she was right about who to hire led her to have some animosity towards me from the very beginning. I don't report to her but she is my senior and I do need to work with her quite frequently.

The tone of her emails have a hint of superiority where she thinks I'm a complete idiot for asking questions I should be asking and should be asking her. I want to note that she is difficult to work with and this is widely known within the company, so it's not just me but she while she treats many people in a similar manner, the way that poor way she treats me is amplified compared to others.

I know arguing with her and correcting her will only backfire. When she says out of line things I just ignore it. When she skims an email and completely misreads what I'm asking yet replies with something that isn't related to the initial email I ignore it.

This isn't working to help improve the relationship. Any thoughts as to how to deal with this type of older woman?