Related Topics:

Matrices

Inverse of a 2×2 Matrix

Determinant of a 3×3 Matrix

### Determinant of a 2×2 Matrix

**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.

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

**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 or is degenrate and does not have an inverse such that:

AA = I

**Further lessons on determinants of matrices**

**Another video on the determinant of a 2×2 matrix**

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

Matrices

Inverse of a 2×2 Matrix

Determinant of a 3×3 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.

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

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

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* Example: *

* Solution: *

* Example: *

* Solution: *

Examples:

1. Check whether a matrix is singular.

2. Given that the value of the determinant of A is 24, find w.

One example contains fractions.

If det(A) = 0, the matrix is singular. This means it is not invertible or is degenrate and does not have an inverse such that:

AA

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You can use the free Mathway calculator and problem solver below to practice Algebra or other 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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