Finding 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
The inverse of a matrix is often used to solve a system of linear equations can be represented in matrix form. These lessons and videos help Algebra students find 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:
- Calculate the determinant (ad - bc).
- Swap a and d, and change the signs of b and c.
- Multiply the modified matrix by 1 divided by the determinant.
- 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.
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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