The inverse of a 2 x 2 matrix - Matrices

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.

Lessons

Notes:
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 X1X^{-1}, and so we can say that
XX1=IXX^{-1}=I

Let XX be a matrix and you want to find the inverse (denote as X1X^{-1} ). Then we use the following formula:
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The inverse of a 2 x 2 matrix

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