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# Finding the Inverse of a Matrix

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In this lesson, we learn how to find the inverse of a matrix. When a square matrix has an inverse, it is known as invertible or nonsingular. When we want to find the inverse of a nonsingular square matrix A, we set up the following augmented matrix:

[A | I]

Where A is on the left and the identity matrix of the same order is on the right. Basically, we can use row operations to transform the augmented matrix into the following form:

[I | A

Now we will have the identity matrix on the left and the inverse of A on the right. We will also learn that when finding the inverse of a 2 x 2 matrix, there is a simple shortcut that we can employ.

[A | I]

Where A is on the left and the identity matrix of the same order is on the right. Basically, we can use row operations to transform the augmented matrix into the following form:

[I | A

^{(-1)}]Now we will have the identity matrix on the left and the inverse of A on the right. We will also learn that when finding the inverse of a 2 x 2 matrix, there is a simple shortcut that we can employ.

Finding the Inverse of a Matrix:

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