Question on binary operation?

Question

let * be a binary operation on a set S.

Assume (a*b)*a = b for all a,b belongs to S. Prove that a*(b*a) = b for all a,b belongs to S.

Answer 1

(1): (a*b)*a = b
Substitute 'b' for 'b*a' in (1) then
(2): (a*(b*a))*a = b*a => a*(b*a) = b
Q.E.D.

Answer 2

Binary operation is a mathematical operation wherein 2 factors are blended to yield a unmarried consequence. Please locate bellow some examples: Decimal a million is binary 001; Decimal 3 is binary 0011; Decimal 6 is binary 0110; Decimal 9 is binary 1001.

Answer 3

the question kinda makes no sense but it might in all make perfect sense im not exactly sure you can even put most of that into a binary form

Answer 4

Let x, y in S.

Apply the rule with a = y * x, b = y:
y = [(y * x) * y] * (y * x)

Now apply it to the first argument with a = y, b = x:

y = x * (y * x)

which had to be proven.

Answer 5

man i got the same question.