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**

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.

.

* Example: *

* Solution: *

* Example: *

* Solution: *

(1 × *x*) − (4 × −2) = 5

*x* + 8 = 5

*x* = −3

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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