# Finding the Determinant of a 2×2 Matrix

Related Topics:
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.

### 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.

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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

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