Algebra as Structure Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
What is the identity element for addition? For multiplication?

Solution

  1. 1
    Addition: a+0=aa + 0 = a, so the identity is 00.
  2. 2
    Multiplication: a×1=aa \times 1 = a, so the identity is 11.

Answer

Addition: 00. Multiplication: 11.
An identity element leaves the other operand unchanged. Every algebraic structure has its own identity: 00 for addition, 11 for multiplication, the identity matrix II for matrix multiplication.

About Algebra as Structure

The perspective that algebra is the systematic study of abstract mathematical structures and the operations defined on them.

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