The binary operation □ is defined as a □ b = a + b + ab, where a and b are any two real numbers. The value of the identi...

Question

The binary operation □ is defined as a □ b = a + b + ab, where a and b are any two real numbers. The value of the identity element of this operation, defined as the number z such that a □ z = a for any a, is
A. 0
B. 1
C. 2
D. 10

Accepted Answer

z = 0 An identity element z for a binary operation is one that leaves any operand unchanged. Here the operation a □ b = a + b + ab combines two numbers. We need to find z such that a □ z produces a for every real number a. Substituting and solving gives z = 0.

The binary operation □ is defined as a □ b = a + b + ab, where a and b are any two real numbers. The value of the identity element of this operation, defined as the number z such that a □ z = a for any a, is A. 0 B. 1 C. 2 D. 10