I need to prove that if T is a linear transformation from R^n to R^n, which in onto, then T is invertible.
I am not sure where to begin. Any help would be great.
Are you allowed to use the "rank-nullity" theorem, that if A:U->V then the dimension of AU plus the dimension of the kernel of A is equal to the dimension of U? If A is "onto" , its rank is n. Since the A is from , its nullity is n- n= 0 so A is also "one to one".