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 Pages**

Determinant of a 2×2 Matrix

Singular Matrix

Inverse of a 3×3 Matrix.

More Lessons On Matrices

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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