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# Determinant Calculator

Enter the values of the matrix to calculate the determinant of a matrix using determinants calculator.

This matrix determinant calculator can calculate the determinants of matrices up to the order of 5. What’s amazing about this calculator is that you can see all the steps of calculations.

## Definition - Determinant of a Matrix

Determinants are scalar quantities and are functions of square matrices. They help to know the nature and inverse of matrices.

A determinant is usually represented with capital alphabets. It is a function of a matrix that gives a singular value.

## Formula to find determinant of matrix

Square matrices exist in various sizes. Each size has a different formula of determinants. It is not possible to write formulas for all. So below are the formulas for the most common ones.

**For a 2x2 matrix**

**For a 3x3 matrix**

The expansion method for the above equation:

## How to find determinant of a matrix?

**Example**

Find the determinant of the following matrix:

**Solution:**

**Step 1: **Write down the formula.

= (a x d) - (c x b)

**Step 2:** Place the values in the equation.

=(4 x 2) - (3 x 6)

= 8 - 18

**= -10 **