Can a Transformation Matrix be one-to-one and not onto?

[suchara]

Title says all..
A transformation matrix is one to one if its columns are linearly independant, meaning it has a pivot in each column
but what if it doesn't have a pivot in each row(i.e. not onto)? is it still one-to one?

 

[suchara]

actually nvm,... I just realized it will map an Rⁿ vector onto R^m where m < n, but its still one-to-one