# Identity Matrices

In these lessons, we will learn about the identity matrix and inverse matrices.

We also feature a matrix calculator that will help you to find the inverse of a 3×3 matrix. Use it to check your answers.

A square matrix, I is an identity matrix if the product of I and any square matrix A is A.
i.e. IA = AI = A

For a 2 × 2 matrix, the identity matrix for multiplication is When we multiply a matrix with the identity matrix, the original matrix is unchanged.  If the product of two square matrices, P and Q, is the identity matrix then Q is an inverse matrix of P and P is the inverse matrix of Q.
i.e. PQ = QP = I

The inverse matrix of A is denoted by A-1. (read as “A inverse”)

AA-1 = A-1A = I

Note that the inverse of A-1 is A.

Example: Given that B is the inverse of A, find the values of x and y.

Solution:
AB = Since B is an inverse of A, we know that AB = I 1 – 2y = 1
2y = 0
y = 0

2x = 1
x = The Identity Matrix
This video introduces the identity matrix and illustrates the properties of the identity matrix.

A n × n square matrix with a main diagonal of 1’s and all other elements 0’s is called the identity matrix In.

If A is a m × n matrix, then ImA = A and AIn = A.
Is A is a n × n square matrix, then
AIn = InA = A.

Determining a 2×2 Inverse Matrix Using a Formula
This video explains the formula used to determine the inverse of a 2x2 matrix, if one exists.

Example:
Determine the inverse of matrix A.

How to find the inverse of a 2×2 matrix using the inverse formula?

Identity matrix and inverse matrix

This matrix calculator will help you find the inverse of a 3×3 matrix.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 