# Calculate Determinant of a Matrix

This is a tutorial on how to calculate the determinant of a 2 by 2 matrix and that of a 3 by 3 matrix. Check answers using these online calculators to calculate the determinant of a 3 by 3 Matrix and the determinant of 2 by 2 Matrix.

## Determinant of a 2 by 2 Matrix

The determinant of the 2 by 2 matrix A

is a scalar given by

Example 1: Find the determinant of the 2 by 2 matrix A given by

Solution

det(A) = -2*(1/2) - 5*3 = -16

Check your answer using this calculator of determinant of a 2 by 2 Matrix.

## Determinant of a 3 by 3 Matrix

The determinant of the 3 by 3 matrix A

is a scalar given by

Example 2: Find the determinant of the 3 by 3 matrix A given by

Solution

det(A) = 2(5*5-4*1) - (-1)*(-2*5 - 4*0) + 3*(-2*1 - 5*0) = 42 - 10 -6 = 26

Check answer using this online calculator to calculate the determinant of a 3 by 3 Matrix

References and links related to dterminants and systems of equations.

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Updated: 2 April 2013