Question

prove that the set of all 2 * 2 matrix form an abelian group w.r.t matrix addition
​

Answer 1

=I , [

−1

0

0

−1

]=−I . Let [

−1

0

0

1

]=a and [

1

0

0

−1

]=b

Given matrices are invertible, Therefore they satisfy invertibility property

Observe that given matrices satisfies commutative property ( Ia=aI=a , bI=Ib=b , −Ia=a(−I)=−a , −Ib=b(−I)=b , ab=ba , I(−I)=(−I)I=−I )

Therefore it also satisfies associative property

Hence the given matrices form an abelian group , under multiplication of matrices.

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