Matrix Determinant Calculator (2×2)

Enter the 4 values of your 2×2 matrix into the calculator. The calculator will evaluate and display the matrix determinant.

Matrix Determinant Calcualtor

The following formula is used to calculate the determinant of a 2×2 matrix.

Given the matrix in the form:


The determinant can be calculated using the following:


  • Where a,b,c,d are the values of the matrix

Example Problem

  1. Let’s assume we are given a matrix of size 2×2 with values of 4,5,6,7 for A, B, C, and D respectively.
  2. To calculate the determinant, first, we should confirm the values of the matrix with the table above. For example, make sure that the value for A is in the top left-hand corner of the matrix.
  3. Next, we input the values into the formula a*d-b*c = 4*7-5*6 = -2.
  4. Use, the resulting determinant to help solve your application.


What is a matrix determinant?

A matrix determinant is a measure of the “magnitude” of a matrix of values. This magnitude is used to calculate the values in systems of linear equations.

What does a matrix determinant tell you?

A matrix determinant is a single value that is often related to the area or volume of a region. The value shows how much the specific matrix will scale or reflect objects in a linear transformation.

What are matrices used for?

Matrices are used in many fields of mathematics and physics. Some more commonly known uses are those in the application of electricity.

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