Question
PROBLEM e
1.) In the following exercises, a set S and a definition for * are given. Answer each of the following. - Prove or disprove t

Definition: A GROUP is a set S paired with an operation *, denoted <S,*> satisfying the four properties;

G0: CLOSURE - For any a, b in S, a * b in S

G1: ASSOCIATIVITY - For all a, b, c in S, (a * b) * c = a * (b * c)

G2: IDENITY - There exists an element e in S such that a * e = e = b * a, for all a in S

G3: INVERSION CLOSURE - For each a in S, therr exists some b in S such that a * b = e = b * a , where b is the inverse of a.

e. S = {A E M (R): A is diagonal}, where A + B = A + B f. S = {A E Mn(R): A is diagonal and has no zero diagonal entry}, wher


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Answer #1

O S=> AE MH CIR): A is diagonal * is defined by AHB = ATB . Let A and B Se diagonal matrix then (A&B) also diagonal matrix To

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