Matrices—Operations and Inverses

Lesson Objective

In this lesson, you will review matrices and their operations. You will also identify the properties of operations on matrices and explore inverses.


A matrix is a rectangular array of numbers. The numbers in a matrix are referred to as the elements of a matrix.

A matrix is made up of rows and columns. The dimensions of the matrix are said to be “m by n” which is written m × n. An m × n matrix has m rows and n columns. This notation does not mean that you multiply m by n.

A 1 × n matrix is sometimes called a row vector.

A m × 1 matrix is sometimes called a column vector.


A is a 3 × 2 matrix, while both B and C are 2 × 2 matrices.

The number 2 is the entry for a11, b21, b22, and c12.

Two matrices A and B are equal if A and B have the same dimensions, and every entry aij is equal to every entry bij.

The two matrices P and Q shown below are equal. Notice that they are both 2 × 3 matrices and their respective entries are equal to each other.


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