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

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

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