Lesson Plan: Properties of Matrix Multiplication Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to identify the properties of matrix multiplication, including the transpose of the product of two matrices, and how they compare with the properties of number multiplication.


Students will be able to

  • understand that “𝐼” is the multiplicative identity for matrices,
  • understand the distributive property of matrix multiplication,
  • understand the associative property of matrix multiplication,
  • understand the conditions required for matrix multiplication to be commutative,
  • understand interactions between the properties of matrix multiplication and transposition (i.e., (𝐴𝐵)=𝐵𝐴).


Students should already be familiar with

  • the required conditions for the multiplication of two matrices to be well defined,
  • matrix multiplication (of 3×3 matrices or smaller),
  • scalar matrix multiplication,
  • diagonal matrices,
  • the transpose of a matrix.


Students will not cover

  • determinants,
  • finding the multiplicative inverse of a matrix.

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