Double Math

# Determinant of 2×2 Matrix

In absolute-value bars instead of square brackets, determinants are based on square matrices. In an advanced course, you’ll likely learn more about determinants, as there is a lot you can do with them. The purpose of this lesson is simply to demonstrate how to compute 2×2 and 3×3 determinants. This method can be extended to calculate larger determinants, but that is more complicated.

Given a matrix named “B“, the determinant of B is denoted by “det(B)”, pronounced as “the determinant of B“, or just “det-B”.

Only square matrices can be used to derive determinants. In general, if your matrix isn’t square then it does not have a determinant (some people have tried to define pseudo-determinants for non-square matrices, but others don’t seem to be catching on. You’ll only hear about determinants for square matrices. Because of reasons.) If your matrix isn’t square, it does not have a determinant.

## How to find the determinant of a 2-by-2 matrix?

Subtract its diagonal products to find the matrix’s determinant.

A=\begin{vmatrix}\begin{array}{cc}a&b\c&d\end{array}\end{vmatrix}.

the matrix A with variables:

To take the determinant of a 2×2 matrix,  follow these steps:

1. A diagonal multiplying operation is performed by multiplying the values along the top-left and bottom-right axes
2. The diagonal is multiplied by the bottom-left and top-right values
3. By subtracting the second product from the first, we get
4. Determining the 2-by-2 determinant by simplifying.

## Can a determinant be negative?

Yes, determinants can have negative values.

The definition of determinants is similar to the definition of absolute values, and they are expressed in the same notation. However, they are not the same, and determinants can in fact be negative as well.