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A group is a set G together with a multiplication, which satisfies three properties. A multiplication is a binary operator : G times G
A group is a set G together with a multiplication, which
satisfies three properties. A multiplication is a binary operator
: G times G G
which takes two inputs from G and returns one output from G The three properties that the
multiplication is required to satisfy are the following:
for all elements g h k in G of G we have g h k g h k
there exists an element G in G such that for all g in G we have g G G g g
for all elements g in G there exists g in G such that g g g g G
This structure is absolutely central in mathematics since its introduction in the th century.
In this exercise, your task will be to show that the following set of matrices is a group under
matrix multiplication
G :
a b
c
a b c in R
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