Welcome to MHF, cristi92!
That looks fine to me!
where A is a bijective linear transformation, is the set of polynomials with real coeficients and max degree=2 .
To do this I have to find the matrix of A relative to canonical basis of and , find the inverse of that matrix and then is the answer I'm looking for.
Please tell me if I am right or not.
That would work but since you are NOT asked to find either A or in general, it would seem easier to me to state the problem as "find numbers, a, b, c, so that , such that , , ". In other words solve the three equations a- b+ c= 0, c= 6, a+ b+ c= 0 for a, b, and c.
Of course, if you solve those equations by setting up the matrix of coeffients and row-reducing, you are doing what you describe but those are particularly easy equations to solve.