# Finding the Inverse of a 2×2 Matrix

The inverse of a matrix is often used to solve matrix equations. These lessons and videos help Algebra students find the inverse of a 2×2 matrix.

### Inverse of a 2×2 Matrix

Let us find the inverse of a matrix by working through the following example:

Example: Solution:
Step 1: Find the determinant. Step 2: Swap the elements of the leading diagonal. Recall: The leading diagonal is from top left to bottom right of the matrix.

Step 3: Change the signs of the elements of the other diagonal. (Change the signs of 8 and 5)

Step 4: Divide each element by the determinant.  When a matrix has no inverse it is called a singular matrix.

Inverse Matrices
If AB = BA = I, then A and B are inverse matrices.

Finding Inverse of a 2×2 Matrix

Example:
Find A-1, the inverse of matrix A

How to find the inverse of a 2×2 matrix?

Determinant and inverse of 2×2 matrix

What is meant by the identity matrix and how to find the inverse of a matrix?

Singular Matrices

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