Doubt about the best way to calculate the inverse matrix in my case

Hi! During my calculus, I have to solve a matricial equation of the type Ax=b.
I thought to simple obtain the inverse of matrix A (10 x 10) to calculate the vector x. First, I used the A.Invert() command, but there is a more direct way to solve the equation without calculating the inverse matrix?
I read the page ROOT: tutorials/matrix/invertMatrix.C Source File and I realized there are several manners to calculate the inverse matrix. I`am using the LU decomposition and I tested the results by the definition of the inverse matrix (A*A^{-1} = A^{-1}*A = Identity). The outcome is OK!

I guess @moneta can help.

Have a look at solveLinear.C and the Solve methods available in all the decompose classes