The Total solution for NCERT class 6-12
Show that the binary operation * on Z defined by a * b = 3a + 7b is notcommutative?
Let a, b ∈ Z
a * b = 3a + 7b
b * a = 3b + 7a
Thus, a * b ≠ b * a
Let a = 1 and b = 2
1 * 2 = 3 × 1 + 7 × 2
= 3 + 14
= 17
2 * 1 = 3 × 2 + 7 × 1
= 6 + 7
= 13
Therefore, there exista = 1, b = 2 ∈ Z such that a * b ≠ b* a
Thus, * is notcommutative on Z.