Finding the Determinant of a 2×2 Matrix

Determinants are useful properties of square matrices, but can involve a lot of computation.

A 2×2 determinant is much easier to compute than the determinants of larger matrices, like 3×3 matrices. To find a 2×2 determinant we use a simple formula that uses the entries of the 2×2 matrix. 2×2 determinants can be used to find the area of a parallelogram and to determine invertibility of a 2×2 matrix.

To find the determinant of a 2x2 matrix:

1. Multiply the top-left element by the bottom-right element.
2. Multiply the top-right element by the bottom-left element.
3. Subtract the second product from the first product.

If the determinant of a matrix is 0 then the matrix is singular and it does not have an inverse.

 

Determinant of a 2×2 Matrix

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

Example:

 

Solution:

 

Example:

 

Solution:
(1 × x) − (4 × −2) = 5
x + 8 = 5
x = −3

How to find the determinant of a 2×2 matrix, and solve a few related problems?

Examples:

1. Check whether a matrix is singular.
2. Given that the value of the determinant of A is 24, find w.

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Explains the formula used to determine the inverse of a 2×2 matrix, if one exists

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Two examples of calculating a 2×2 determinant
One example contains fractions.
If det(A) = 0, the matrix is singular. This means it is not invertible and does not have an inverse such that: AA = I

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Further lessons on determinants of matrices

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Another video on the determinant of a 2×2 matrix

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Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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