find the order of GL(2,R), where R is the group of integers modulo 3. As a hint,
ID: 2961488 • Letter: F
Question
find the order of GL(2,R), where R is the group of integers modulo 3. As a hint, it is helpful to consider the cases where a matrix has 0,1,2,3, or 4 zeros separately. Afterwards, spend some time thinking about other cases for R (integers mod 4, mod 5, mod p, etc.) The total number of possible matrices increases very quickly. Generalizing for any modulus (prime or composite) is probably too difficult, but I would like each of you to write down any observations that you made which would help in narrowing down the possibilities for the order of the group.
Explanation / Answer
integer modulo 3 are 0,1,2 so for each of the four elements there is four options. so order of GL(2,R)=3^4=81 when R-integers mod 3..
in general when R is integers mod n then order of GL(2,R) is n^4
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.