The Inverse of a 2 x 2 matrix

The Inverse of a 2 x 2 matrix

In this lesson, we will learn how to find the inverse of a 2 x 2 matrix. You will learn that if two matrices are inverses of each other, then the product of the two matrices will result in an identity matrix. Next, you will learn how to find the inverse by using the formula below. You may find that the formula is hard to memorize. There is another way to find a 2 x 2 matrix without memorizing the formula, but it would require matrix row operations. You will see this method in the section "the inverse of 3 x 3 matrices with matrix row operations". Lastly, note that the inverse of a 2 x 2 identity matrix is just the identity matrix itself.
Basic Concepts: Notation of matrices, Matrix multiplication, The determinant of a 2 x 2 matrix

Lessons

Let the matrices XX and YY be inverses. Then that means the following is true:
XY=IXY=I
where II is the identity matrix. To be more precise, we can say that since XX and YY are inverses, then YY is the same as X−1X^{-1}, and so we can say that
XX−1=IXX^{-1}=I

Let XX be a matrix and you want to find the inverse (denote as X−1X^{-1} ). Then we use the following formula:
formula for finding the inverse of a matrix
  • Introduction
    The Inverse of a 2 x 2 matrix overview:
    a)
    Are the two matrices inverses?

    b)
    Finding the inverse of a 2 x 2 matrix

  • 1.
    Checking if the two matrices are inverses
    Check that The Inverse of a 2 x 2 matrix and The Inverse of a 2 x 2 matrix are inverses.
  • 2.
    Check that The Inverse of a 2 x 2 matrix and The Inverse of a 2 x 2 matrix are inverses.
  • 3.
    Check that The Inverse of a 2 x 2 matrix and The Inverse of a 2 x 2 matrix are inverses.
  • 4.
    Finding the inverse of a matrix
    Find the inverse of the matrix The Inverse of a 2 x 2 matrix
  • 5.
    Find the inverse of the matrix The Inverse of a 2 x 2 matrix
  • 6.
    Find the inverse of the matrix The Inverse of a 2 x 2 matrix
  • 7.
    Find the inverse of the matrix The Inverse of a 2 x 2 matrix
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51.
Determinants and Inverses of Matrices
51.1
The determinant of a 2 x 2 matrix
51.2
The determinant of a 3 x 3 matrix (General & Shortcut Method)
51.3
The inverse of a 2 x 2 matrix
51.4
The inverse of 3 x 3 matrices with matrix row operations
51.5
The inverse of 3 x 3 matrix with determinants and adjugate
51.6
2 x 2 invertible matrix
51.7
Solving linear systems using Cramer's Rule
51.8
Solving linear systems using 2 x 2 inverse matrices
ACCUPLACER Test Prep