Determine whether multiplication by a is one to one linear transformation
a)a=[ 1 -1
2 0
3 -4]
b) a=[ 1 2 3
-1 0 4]

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 :)