We consider the group G {\displaystyle {}G} of invertible 2 × 2 {\displaystyle {}2\times 2} -matrices over the field Z / ( 3 ) {\displaystyle {}\mathbb {Z} /(3)} with 3 {\displaystyle {}3} elements, and the subgroup H {\displaystyle {}H} of all invertible matrices with determinant 1 {\displaystyle {}1} . Which of the following matrices are equivalent to each other (with respect to H {\displaystyle {}H} ), and which are not?
of
invertible
-matrices
over the
field
with 
elements, and the subgroup 
of all invertible matrices with
determinant
. Which of the following matrices are
equivalent
to each other
(with respect to ),
and which are not?
