Determinant Calculator

The determinant of a matrix calculator is designed to calculate and provide the complete solution for 2x2 or 3x3 square matrix determinant value with one click. 

It reduces the given matrix to row echelon form and multiplies the main diagonal elements to complete the calculation.

What is the determinant of a matrix?

A matrix is a rectangular array of multiple numbers arranged in a specific order of rows and columns. For a square matrix, you can easily get the information related to the matrix just in a single number, called the “Determinant.”

It is a function whose input is a square matrix and a result is a number. The determinant of a matrix “A” is a specific real number, an attribute of the matrix A and denoted by |A| or det(A).

How to find the determinant of a matrix?

The calculator can easily find out the determinant by using Cramer’s rule of expansion by minors or with the row reduction expansion method.

You can find the determinant of a matrix manually. Let's look at an example of a matrix to solve for its determinant.
Example:
Step #1:  \(A =\begin{vmatrix} 3 & 5 & 7 \\ 1 & 2 & 4\\ 4 & 8 & 3\end{vmatrix} \)

Step #2: \(|A| =\begin{vmatrix} 3 & 5 & 7 \\ 1 & 2 & 4\\ 4 & 8 & 3\end{vmatrix} \)

Step #3: \(|A| = 3\begin{vmatrix} 2 & 4 \\ 8 & 3 \end{vmatrix} - 5\begin{vmatrix} 1 & 4 \\ 4 & 3 \end{vmatrix} + 7 \begin{vmatrix} 1 & 2 \\ 4 & 8 \end{vmatrix}\)

Step #4: \(|A| = 3 (2\times 3-4 \times 8)-5(1 \times 3- 4 \times 4)+7(1 \times 8- 2 \times 4)\)

Step #5: \(|A| = 3(-26)-5(-13)+7(0)\)

Step #6: \(|A| = -78+65+0\)

Step #7: \(|A| = -13\)