$x^TAx>0$ means that matrix is positive definite. And properties of positive definite matrix (relevant to question) is :
- All its eigen values are positive.
Let's consider a $3*3$ matrix for simplicity.
- Trace(A) = sum of eigen values = positive
- Det(A) = product of eigen values = positive
Take any matrix and try to anlayse the validity of these points.
So, (E) is the answer here.