Let A= (1/3 1/3 1/3)^T. Think of A as an operator from R^1(a one roll matrix with real number) to R^3(a matrix with 3 rows and one column) via matrix vector multiplication.

My questions are that how can I show that

1) the operator is one to one

2) how can i find 2 linear left- inverses for A

3) how can i find a left inverse for A that is not linear

A= (1/3 1/3 1/3)^T this, T mean transpose

Plz help