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

We also have a matrix calculator that will help you to find the inverse of a 3x3 matrix. Use it to check your answers.

Related Topics:

More Lessons on Matrices

A square matrix,**I** is an **identity matrix** if the product of **I** and any square matrix **A** is **A**.

**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 I_{n}.

If A is a m × n matrix, thenI_{m}A = A and AI_{n} = A.

Is A is a n × n square matrix, then

AI_{n} = I_{n}A = A.
**Determining a 2x2 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 2x2 matrix using the inverse formula?**

**Identity matrix and inverse matrix**

This matrix calculator will help you find the inverse of a 3x3 matrix.

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

We also have a matrix calculator that will help you to find the inverse of a 3x3 matrix. Use it to check your answers.

Related Topics:

More Lessons on Matrices

A square matrix,

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**^{-1}**A** = **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 – 2

y= 1

2y= 0

y= 02

x= 1

x=

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 I

If A is a m × n matrix, thenI

Is A is a n × n square matrix, then

AI

This video explains the formula used to determine the inverse of a 2x2 matrix, if one exists.

Example:

Determine the inverse of matrix A.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

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

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