How to calculate the inverse of a 2x2 matrix

Before going to see how to find the inverse of a 2x2 matrix, let us recall the meaning of inverse. In general, the inverse of a real number is a number which when multiplied by the given number results in the multiplicative identity, which is 1. In matrices, the inverse of a matrix A which is denoted by A -1 is a matrix which when multiplied by A gives the identity matrix, I. But how to find the inverse of 2x2 matrix?

In mathematics, a matrix is an ordered rectangular array of numbers or functions. The numbers or functions are called the elements or the entries of the matrix. Some matrices may contain inverse and some may not. In that case A is said to be invertible. In this article, you will learn how to find the inverse of a 2 x 2 matrix using different methods. To find the inverse of any matrix, it is important to observe that the determinant of the matrix should not be 0. If the matrix determinant is equal to zero, then the inverse of that matrix does not exist.

How to calculate the inverse of a 2x2 matrix

If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Donate Log in Sign up Search for courses, skills, and videos. Finding inverses of 2x2 matrices. About About this video Transcript. Sal gives an example of how to find the inverse of a given 2x2 matrix. Created by Sal Khan. Want to join the conversation? Log in. Sort by: Top Voted. Posted 11 years ago. What if the determinant is 0? Is the answer undefined? Downvote Button navigates to signup page.

You are right. Is the answer undefined?

Please read our Introduction to Matrices first. Reciprocal of a Number note: 1 8 can also be written 8 Inverse of a Matrix. When we multiply a matrix by its inverse we get the Identity Matrix which is like "1" for matrices :. The inverse of A is A -1 only when:. So, let us check to see what happens when we multiply the matrix by its inverse:. Because with matrices we don't divide!

Before going to see how to find the inverse of a 2x2 matrix, let us recall the meaning of inverse. In general, the inverse of a real number is a number which when multiplied by the given number results in the multiplicative identity, which is 1. In matrices, the inverse of a matrix A which is denoted by A -1 is a matrix which when multiplied by A gives the identity matrix, I. But how to find the inverse of 2x2 matrix? Let us see the formula for finding the inverse of 2x2 matrix along with some other ways of finding it. Here, we can also see some examples of finding the inverse of a 2x2 matrix. The inverse of a 2x2 matrix formula uses the determinant of the matrix. The adjoint of a matrix A is the transpose of the cofactor matrix of A. But for finding the adjoint of a 2x2 matrix, we don't need to have the headache of finding cofactors. There is a trick to find the adjoint of a 2x2 matrix.

How to calculate the inverse of a 2x2 matrix

The inverse of a matrix is significant in linear algebra. It helps us solve a system of linear equations. We can find the inverse of square matrices only. Some matrices do not have inverses. So, what is the inverse of a matrix? There will be a lot of examples for you to look at. Practice problems will follow. Happy learning!

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Dipesh Chaudhary. Breakdown tough concepts through simple visuals. Inverse of 2x2 Matrix Before going to see how to find the inverse of a 2x2 matrix, let us recall the meaning of inverse. So the negative-- let me do a new color. There is a trick to find the adjoint of a 2x2 matrix. Class 11 Maths Index. Difference Between Ln And Log. Wall of Words. Maths Formulas. Want to join the conversation? Calculations like that but using much larger matrices help Engineers design buildings, are used in video games and computer animations to make things look 3-dimensional, and many other places. Please read our Introduction to Matrices first.

In mathematics, a matrix is an ordered rectangular array of numbers or functions. The numbers or functions are called the elements or the entries of the matrix.

The inverse of a 2x2 matrix formula uses the determinant of the matrix. And then the adjugate of A-- and here I'm really just teaching you the mechanics of it. Watch Now. Imagine we can't divide by numbers Donate Log in Sign up Search for courses, skills, and videos. Maths Puzzles. Therefore, B -1 exists. If it is zero, then the matrix has no inverse and in that case, it is called a singular matrix. The matrix B will be the inverse of A. Before going to see how to find the inverse of a 2x2 matrix, let us recall the meaning of inverse. Commercial Maths. Comment Button navigates to signup page. Chuck Towle. Downvote Button navigates to signup page.