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.

 

Learn to find the determinant of a 3x3 matrix

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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