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1. Determine in each of the following cases, whether the described system is or not a...

1. Determine in each of the following cases, whether the described system is or not a group. Explain your answers. Determine what of them is an Abelian group.
a) G = {set of integers}, a* b = a − b
b) G = {set of matrices of size 2 × 2}, A * B = A · B
c) G = {a0, a1, a2, a3, a4}, ai * aj = a|i+j|, if i+j < 5, ai *aj = a|i+j−5|, if i+j > 5, for i, j=0,1,2,3,4.
d) G = R* = {Real numbers except 0}, a ∗ b = −5ab.

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