Question 32
Binary OperationsThe table shows the operation * on the set {x, y, z, w}.
Row x: x * x = y, x * y = z, x * z = x, x * w = w
Row y: y * x = z, y * y = w, y * z = y, y * w = x
Row z: z * x = x, z * y = y, z * z = z, z * w = w
Row w: w * x = w, w * y = x, w * z = w, w * w = z
Find the identity element.
- A.x
- B.y
- C.z
- D.w
Show the answer and explanation
Answer: C (z)
Explanation
Row z and column z reproduce the other element every time (z * a = a * z = a), so z is the identity.