Let $F_q$ be a finite field with $q$ elements. Consider $F^2_q$ and $F^4_q$ as $F_q$ vector spaces. Calculate the number of one-to-one linear transformations $T$ : $F^2_q$ → $F^4_q$ (in terms of $q$).
From my calculations I got $(q^4-1)(q^4-q)$. But I am not sure of it.
Can anyone help with justification also!!