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## Definition of Identity

• Identity Equation: An equation which is true for every value of the variable is called an identity equation. Examples of identity equation:

5(a - 3) = 5a - 15,

• Identity Inequality: An inequality which is true for every value of the variable is called an identity inequality. For example, the inequality   is true for every value of a.

• Identity Function: A function in which the domain values doesn't change at all.

f (x) = x is an identity function.

are identity matrices of dimension 2 × 2 and 3 × 3 respectively. The product of n × n matrix and the identity matrix gives back the n × n matrix.

Solved Example on Identity

Solve the equation 5(x + 2) = 5x + 10 and determine whether it has one solution, no solution, or is an identity.

Choices:

A. an identity

B. one solution

C. not enough information given

D. no solution

Step 1: 5(x + 2) = 5x + 10        [Given equation.]

Step 2: 5x + 10 = 5x + 10        [Multiply 5 to remove the parenthesis.]

Step 3: 5x + 10 - 5x = 5x + 10 - 5x    [Subtract 5x from each side.]

Step 4: 10 = 10                         [Combine like terms.]

Step 5: 10 = 10 is always true. So, the given equation is an identity.

Related Terms for Identity

• Identity Equation
• Identity Inequality
• Identity Matrix
• Identity Function
• Matrix
• Variable
• Inequality
• Equation
• Element