Properties of matrix multiplication

The  exercise appears under the Precalculus Math Mission. This exercise explores some of the properties of matrix multiplication.

Types of Problems
There are two types of problems in this exercise:


 * 1) Which expression is the same value: This problem has a matrix expression and several other potential forms of the expression. The student is expected to select which of the options would evaluate to the same result.Pomm1.png
 * 2) Fill in the matrices and answer the question: This problem provides a couple matrix expressions. The student is expected to find the result of the expressions and use the results to answer a question about matrix multiplication properties.Pomm2.png

Strategies
Knowledge of the matrix representation of geometric transformations is encouraged to ensure success on this exercise.
 * 1) Matrix multiplication is associative.
 * 2) Matrix multiplication is not commutative.

Real-life Applications

 * 1) Matrices are the foundational concept in linear algebra.
 * 2) Matrices can be a method for efficiently solving systems of linear equations.
 * 3) Matrices can be viewed as an extension of a number system.