Matrix Operations and Properties

Start with matrix structure

The resources on this page offer several ways into matrix operations and properties. For an overview, start with a Matrices mind map. One describes a matrix as a rectangular array of numbers, with rows, columns and an order. Another covers matrix sizes and types, including row, column, square and diagonal matrices.

These maps give you terms to look for as you move on to questions. The flashcards on matrix algebra also ask how to state a matrix's order and when matrices can be added or subtracted. Use them to check whether you can explain those ideas in your own words.

Move from maps to questions

After reviewing the maps, try the slides titled Matrices Questions. They contain questions on addition, subtraction and multiplication, as well as an expression involving multiples of matrices. Work through a question, then return to a map or the matrix algebra flashcards when you want to review a term or operation.

For a focused activity, use Matrix Multiplication Questions. The quiz asks you to drag values into answers to multiplication questions. A Matrices mind map also covers multiplying matrices, so it can serve as a reference alongside the quiz. Moving between an overview and questions can help you notice which parts you want to study again.

Explore related properties

The collection also includes flashcards on transposes, diagonal matrices and vectors. Another deck asks about invertibility, trace and triangular matrices. These give university students and teachers further material to explore alongside the introductory maps.

This topic is one section of Matrices and Linear Algebra in Mathematics. The page brings its resources together so you can choose a starting point within that unit. Try a multiplication quiz, then return to a map to review the ideas you used.