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.

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.

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?

You can add, subtract, and multiply matrices.

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:.

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?

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? 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.

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Want to join the conversation? You can check your work by multiplying the inverse you calculated by the original matrix. So first let's think about what the determinant of this matrix is. So this element right over here, this 3 will go right over there. But what if we multiply both sides by A -1? So the negative-- let me do a new color. For an invertible matrix of order 2 x2, we can find the inverse in two different methods such as:. In that case A is said to be invertible. Applied mathematicians physicists, computer scientists, engineers etc are often sloppy with mathematical notation. Posted 9 years ago. In that example we were very careful to get the multiplications correct, because with matrices the order of multiplication matters. So how do we solve this one?

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.

Log in. We cannot go any further! Because with matrices we don't divide! Practice Questions on Inverse of 2x2 Matrix. Applied mathematicians physicists, computer scientists, engineers etc are often sloppy with mathematical notation. So first let's think about what the determinant of this matrix is. Donate Log in Sign up Search for courses, skills, and videos. Wall of Words. Linear Equations In One Variable. Before going to see how to find the inverse of a 2x2 matrix, let us recall the meaning of inverse. Calculus Math Apps. Reciprocal of a Number note: 1 8 can also be written 8 Read more: Square matrix Matrix multiplication Determinants and matrices Identity matrix. Posted 11 years ago.