Student question

After finding the loadings it is common to "do a" factor rotation. Analysts "do this" to try to find loadings that are easier to interpret and also note that as long as the rotation is an orthogonal rotation that the estimated covariance/correlation matrix is unchanged. One popular rotation called the varimax rotation. Is this method an orthogonal or an oblique rotation?

When conducting a factor analysis there is one unique set of loading that gives the best set of factors, or there's an infinite set of loadings that will give the same estimated covariance/correlation matrix. What is the correct answer? unique or infinite