2.) Given the binary operation \( a^{*} b=2 a^{2}-6 \). Find \[ \begin{array}{l} a * b=2 \cdot a^{2}-b \\ \text { vate }=23=2(2)^{2}-3 \end{array} \]
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Step 1: Given the binary operation \( a * b = 2a^2 - b \). Show more…
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Madhur L.
A binary operation on a set S is said to be associative if and only if for any elements a, b, and c, Select one: a. a * (b * c) = (c * b) * a b. a * b * c = c * b * a c. (a * b) * c = a * (b * c) d. none of these If S is a set having an identity element "e" with respect to the binary operation * and corresponding to each element "a" in S, there exists an element "b" in S such that Select one: a. a * b = b * a = e b. a + b = b + a = e c. a * e = b * e = e d. a / b = b / a = e
Adi S.
Let * be a binary operation defined on the set of real numbers except zero (R - {0}) by a * b = a + b. (a) Show that * is an associative binary operation. (b) Show that there is a left identity for * and a right inverse for each element in (R - {0}). (c) Show that * is a commutative binary operation. (d) Is (R - {0}, *) a group?
Shaiju T.
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