I am trying to show that

**Z(GL(n,F*)) $\displaystyle \cap$ SL(n,F*)** **$\displaystyle \cong$** **T(n)** ... This is for any non-zero Field

Where Z is the center of General Linear Group.

and

**T(n)={a^n=1 | a $\displaystyle \in$ F*}**

Im trying to figure this out first

** Z(GL(n,F*)) SL(n,F*)**, since the determinant in this set is suppose to be 1, then

**det(aI) = det(a)det(I) = det(a),** this has to be 1 to be in the set therefore

**a=1**, which implies this set contains

**I(n,F*)** (The identity matrix) only.

Am I right so far???

Don't really know what else to do.