Finding the Inverse of a 2×2 Matrix

How to find the Inverse of a 2×2 Matrix?
The following diagram gives the formula used to find the inverse of a 2x2 matrix.

Steps to Find the Inverse:

1. Calculate the determinant (ad - bc).
2. Swap a and d, and change the signs of b and c.
3. Multiply the modified matrix by 1 divided by the determinant.
4. Simplify the fractions (if possible).

When we multiply the matrix with its inverse, we will get the Identity Matrix.

If the determinant (ad - bc) is equal to zero, the matrix does not have an inverse. This is because you cannot divide by zero. Such a matrix is called a singular or non-invertible 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.

Learn how to use the inverse of a matrix to solve a system of linear equations

Inverse Matrices
If AB = BA = I, then A and B are inverse matrices.

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Finding Inverse of a 2×2 Matrix

Example:
Find A^-1, the inverse of matrix A

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How to find the inverse of a 2×2 matrix?

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Determinant and inverse of 2×2 matrix

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What is meant by the identity matrix and how to find the inverse of a matrix?

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Singular Matrices

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