I need to prove that if T is a linear transformation fromR^n toR^n, which in onto, then T is invertible.

I am not sure where to begin. Any help would be great.

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- Sep 18th 2011, 11:13 AMpage929Prove linear transformation is invertible
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. - Sep 18th 2011, 01:52 PMzoekRe: Prove linear transformation is invertible
- Sep 18th 2011, 05:25 PMHallsofIvyRe: Prove linear transformation is invertible
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".