# 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.

Related Topics:
Matrices, Determinant of a 2×2 Matrix, Inverse of a 3×3 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

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