8 . y = 3x - 2 m= b=
2 answers:
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For any arbitrary 2x2 matrices 
and 
, only one choice of exists to satisfy 
, which is the identity matrix.
There is no other matrix that would work unless we place some more restrictions on. One such restriction would be to ensure that is not singular, or its determinant is non-zero. Then this matrix has an inverse, and taking 
we'd get equality.
There is no other matrix that would work unless we place some more restrictions on
Answer:
Lets a,b be elements of G. since G/K is abelian, then there exists k ∈ K such that ab * k = ba (because the class of ab, is equal to
, thus ab and ba are equal or you can obtain one from the other by multiplying by an element of K.
Since K is a subgroup of H, then k ∈ H. This means that you can obtain ba from ab by multiplying by an element of H, k. Thus, . Since a and b were generic elements of H, then H/G is abelian.