Identity
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, (a + b)² = a² + 2ab + b²
• Identity Inequality: An Inequality which is true for every Value of the Variable is called an Identity inequality. For example, the Inequality a² ≥ 0 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.
• Identity Matrix: Its a square matrix with 1 for each element on the main diagonal and 0 for all other elements.
  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
Correct Answer: A
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

Additional Links for Identity

• Click here for samples
• Back to Mathematics Dictionary