The inverse of a matrix A is a matrix that, when multiplied by A results in the identity.

An identity matrix is a matrix equivalent to 1.

There is no concept of dividing by a matrix but, we can multiply by an inverse, which achieves the same thing.

**Formula to calculate inverse matrix of a 2 by 2 matrix.**

We begin by finding the determinant of the matrix.

Swap the positions of the elements in the leading diagonal.

And put a negative sign in front of the elements in the other diagonal.

Lastly, multiply the resultant matrix by 1 divided by the determinant.

**Example:**

Find the inverse of the following matrix.

We begin by finding the determinant of the matrix.

Therefore, the determinant of the matrix is -5.

Then we swap the positions of the elements in the leading diagonal and put a negative sign in front of the elements on the other diagonal.

And lastly, multiply the resultant matrix by 1 divided by the determinant.