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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