Matrix Calculator

The Matrix calculator can find the determinant, the inverse multiply matrices and put a matrix in reduced row echelon form.

Supported operations

Example determinant

Let us say you have a matrix, like this:

$A=\begin{bmatrix}1&2\\3&4\end{bmatrix}$

To find the determinant of Matrix A you do this: you multiply the top left and bottom numbers and then subtract the product of the top right and bottom left numbers. So the determinant of Matrix A is:

$(1)(4)-(2)(3)=-2$

The determinant of Matrix A is -2.

Tips

• You can use numbers or negative numbers in the Matrix calculator.

• If the determinant of Matrix A is zero then Matrix A is singular and the Matrix calculator cannot find the inverse of Matrix A.

• The reduced row echelon form of Matrix A is useful when you want to check if a system of linear equations has a solution.

Sources and further reading

• Wolfram MathWorld: Determinant - definition of the determinant, including the ad - bc rule shown in the 2x2 example.
• Wolfram MathWorld: Matrix Inverse - the inverse exists only when the determinant is nonzero, which is why a singular matrix has no inverse.
• Wolfram MathWorld: Matrix Multiplication - the row-by-column rule used to multiply Matrix A and Matrix B.
• Wolfram MathWorld: Reduced Row Echelon Form - definition of RREF and its use in solving and checking linear systems.
• MIT OpenCourseWare 18.06 Linear Algebra (Gilbert Strang) - free lectures and notes covering determinants, inverses, matrix products, and elimination.