Calculating the Inverse Of A Matrix

Before we can find the inverse of a matrix, we need to first learn how to get the determinant of a matrix.

Determinant Of A Matrix

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Example:

Solution:

Example:

Solution:

Calculate the Inverse of A Matrix

We will show how to calculate the inverse of a matrix by 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.

If the determinant of a matrix is 0 then the matrix has no inverse

It is called a singular matrix.

Example:

Solution:

Determinant = (3 × 2) – (6 × 1) = 0

The given matrix does not have an inverse. It is a singular matrix.

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