FreeMathHelp.com's Matrix Calculator

Perform Matrix Operations Step-by-Step


Type naturally or click in the box to use the math keyboard. Use \begin{bmatrix} for matrices. See examples below for proper syntax.

LaTeX:

Don't rely on any one tool to do all the work for you, and always check your work for correctness!

How does it work?

Enter your matrix expression in the box above using LaTeX notation and click the button to submit. The calculator will identify the operation (multiplication, determinant, inverse, etc.) and show you the step-by-step process. Remember the idea is to *learn* -- not to copy solutions blindly.

This is a brand new feature to FreeMathHelp.com - expect some changes along the way.

Matrix Syntax Guide

Creating a matrix:

\begin{bmatrix} a & b \\ c & d \end{bmatrix}

Use & between elements in a row, and \\ between rows

Try these operations:

  • Matrix Multiplication:
    \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \times \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix}
  • Matrix Addition:
    \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} + \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix}
  • Determinant (2x2):
    det(\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix})
  • Matrix Inverse:
    (\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix})^{-1}
  • Transpose:
    (\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix})^T
  • Scalar Multiplication:
    3 \times \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}

Common Matrix Operations

Here's what this calculator can help you with:

  • Matrix Multiplication: Multiply two matrices (ensure dimensions are compatible)
  • Matrix Addition/Subtraction: Add or subtract matrices of the same size
  • Determinant: Find det(A) for square matrices
  • Matrix Inverse: Find A⁻¹ for invertible matrices
  • Transpose: Flip rows and columns (Aᵀ)
  • Scalar Multiplication: Multiply every element by a number
  • Row Reduction: Convert to row echelon form or reduced row echelon form

Tips for Matrix Input

  • Always use \begin{bmatrix} and \end{bmatrix} to create matrices
  • Use & (ampersand) to separate elements in the same row
  • Use \\ (double backslash) to start a new row
  • Make sure your matrices have compatible dimensions for the operation
  • The virtual keyboard has matrix templates available

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