Practice Algebra as Structure in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

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

Beyond numbers: what happens when ANY set has operations with certain properties?

Example 1

medium
Show that addition of integers and multiplication of integers share a structural property (commutativity).

Example 2

hard
Does matrix multiplication have the same structural properties as number multiplication? Check commutativity.

Example 3

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

Example 4

medium
Does subtraction have an identity element?