Matrix Calculator
Perform matrix operations instantly: addition, subtraction, multiplication, transpose, determinant, inverse, and more. Supports up to 6x6 matrices.
Matrix Calculator
Select an operation and enter matrix values
How to Use
- 1 Set the matrix dimensions using the row and column selectors (1x1 up to 6x6)
- 2 Enter the values for Matrix A by clicking each cell and typing a number
- 3 Select an operation: Add, Subtract, Multiply, Transpose, Determinant, Inverse, etc.
- 4 For operations requiring Matrix B, enter its values in the second grid
- 5 View the result matrix instantly in the preview panel
- 6 Click Copy Result to copy the result matrix to your clipboard
What You Get
Online matrix calculator supporting addition, subtraction, multiplication, scalar multiplication, transpose, determinant, inverse, and matrix power. Handles matrices up to 6x6. All calculations are performed client-side with no data sent to any server.
Input: [[1,2],[3,4]] + [[5,6],[7,8]]
Output: [[6,8],[10,12]]
Input: det([[1,2],[3,4]])
Output: -2
Input: [[1,2],[3,4]]^(-1)
Output: [[-2,1],[1.5,-0.5]]
How do you multiply two matrices?
To multiply matrices A (m x n) and B (n x p), each element of the result is the dot product of a row from A and a column from B. The number of columns in A must equal the number of rows in B. The result is an m x p matrix. For example, for 2x2 matrices: C[0][0] = A[0][0]*B[0][0] + A[0][1]*B[1][0].
How to find the determinant of a 3x3 matrix?
For a 3x3 matrix, use the rule of Sarrus or cofactor expansion. Expand along the first row: det(A) = a11*(a22*a33 - a23*a32) - a12*(a21*a33 - a23*a31) + a13*(a21*a32 - a22*a31). This calculator handles determinants automatically for matrices up to 6x6.
What is the inverse of a matrix?
The inverse of a square matrix A is a matrix A^(-1) such that A * A^(-1) = I (the identity matrix). A matrix has an inverse only if its determinant is non-zero (it is "non-singular"). This calculator finds the inverse using Gauss-Jordan elimination, which is numerically stable for matrices up to 6x6.
What is a transpose of a matrix?
The transpose of a matrix flips it over its diagonal - rows become columns and columns become rows. If A is an m x n matrix, its transpose A^T is an n x m matrix where A^T[i][j] = A[j][i]. For example, the transpose of [[1,2,3],[4,5,6]] is [[1,4],[2,5],[3,6]].
Can you multiply a 2x3 and 3x2 matrix?
Yes! Matrix multiplication is defined when the number of columns of the first matrix equals the number of rows of the second. A 2x3 matrix multiplied by a 3x2 matrix gives a 2x2 result matrix. However, a 2x3 times a 2x3 is NOT possible because 3 does not equal 2.
What is scalar multiplication of a matrix?
Scalar multiplication means multiplying every element of a matrix by a single number (the scalar). For example, if k=3 and A=[[1,2],[3,4]], then k*A = [[3,6],[9,12]]. The dimensions of the matrix stay the same.
When is a matrix not invertible?
A matrix is not invertible (also called "singular") when its determinant equals zero. This happens when the rows or columns are linearly dependent - meaning one row/column can be expressed as a combination of the others. For example, [[1,2],[2,4]] has determinant 0 because the second row is 2 times the first.
Is this matrix calculator free and private?
Yes, this calculator is 100% free with no limits. All calculations happen locally in your browser - no data is ever uploaded to any server. Your matrices are saved in your browser's local storage so you can pick up where you left off.
100% client-side - your data never leaves your device. All matrix operations are performed locally in your browser.