Matrix Calculator
Perform matrix operations including addition, subtraction, multiplication, determinant, inverse, transpose, and rank.
Matrix Inputs
Set matrix dimensions and enter values for Matrix A and Matrix B.
Matrix A
Matrix B
Understanding Matrix Operations
Columns of Matrix A must equal Rows of Matrix B.
Available for square matrices (n × n).
Maximum number of linearly independent row or column vectors.
Frequently Asked Questions (FAQs)
A matrix is square if it has an equal number of rows and columns (e.g., 2×2, 3×3). Determinants and Inverses exist only for square matrices.
Matrix multiplication combines two matrices by multiplying rows of the first matrix with columns of the second matrix. The number of columns in the first matrix must equal the number of rows in the second matrix.
A matrix has an inverse only if it is square and its determinant is not equal to zero. If the determinant is zero, the matrix is singular and cannot be inverted.
The rank of a matrix is the maximum number of linearly independent rows or columns. It indicates the amount of independent information contained in the matrix.
Matrix calculations are widely used in engineering, computer graphics, machine learning, physics, robotics, economics, statistics, and many other scientific and mathematical applications.