To know if the given matrix is one to one linear transformation, Row reduce the Matrix A and if it has free variables in it it means it is not a one to one linear transformation.
So, we take A and apply Row Operation and get the following matrix
1 0 0
0 1 0
0 0 0
As, it has free variables in it, it means it is not a one to one linear transformation.
Hope it helps :)
