Let's say we have two invertible symmetric matrices $A$ and $B$ with same size and same discriminants. (det($A$)/det($B$) is a square of some rational number)
One problem asks me to give an example of this $A$ and $B$ such that the real quadratic spaces constructed by them are isomorphic but the rational quadratic spaces constructed by them are not isomorphic.
I tried several types but can't express such difference: is there any trick to do this?