if Ax=Bx then for every x vector in R^n then A=B
is it true?
True. If $\displaystyle A\neq B$ then $\displaystyle A-B=(c_{ij})\neq 0$ so, there exists $\displaystyle c_{kl}\neq 0$. Choose an adequate $\displaystyle x_0$ such that $\displaystyle (A-B)x_0\neq 0$ or equivalently $\displaystyle Ax_0\neq Bx_0$.
Regards.