The Matrix Calculator builds named matrices and runs determinant, inverse, multiply, transpose, rref, trace, and power operations with clear dimension and singular errors. Results print as bracketed matrices that stay readable beside the editable grid.
Calculate matrix operations online
The Matrix Calculator stores matrices under letters A through H. Choose a name, set rows and columns with New Matrix, and edit cells in the grid. Operation buttons apply to the active matrix or to A and B together for multiply and add. Status text names the operation so a result can be matched to the button that produced it.
Integer and decimal entries are allowed. Output uses the shared number formatter so float noise does not dominate small rational results from an inverse.
Find the determinant of a square matrix
Determinant requires a square matrix. For [[1,2],[3,4]] the Matrix Calculator returns -2. Larger squares use elimination with row swaps tracked in the sign, which keeps the routine stable for classroom sizes up to the UI limit. A non-square active matrix raises a dimension error instead of inventing a determinant.
Trace sits beside det for a quick sum of diagonal entries when only the diagonal matters.
Find the inverse of a matrix
Inverse uses Gauss-Jordan on an augmented [A|I] layout. For [[1,2],[3,4]] the inverse is [[-2,1],[1.5,-0.5]]. When a pivot vanishes within tolerance, the calculator reports no inverse for a singular matrix rather than filling the panel with NaN values.
A^-1 on the keypad targets the active matrix. After a successful inverse, the bracketed result can be copied into later handwritten work or compared with a multiply check A×A^-1.
Multiply and transpose matrices
A×B multiplies store A by store B and checks inner dimensions first. A mismatch prints a clear dimension message and leaves the result panel empty. Transpose swaps rows and columns of the active matrix, so a 2×3 grid becomes 3×2 without rewriting cells by hand.
A+B adds matching shapes only. Scalar-style power A^2 multiplies the active square matrix by itself through the matrix power routine.
Reduce a matrix to row echelon form
rref reduces the active matrix to reduced row echelon form. For a linear system stored as an augmented matrix, the reduced form exposes the solution pattern when one exists. Pivot search uses partial pivoting so near-zero noise is less likely to derail a classroom example.
Use rref when the goal is to solve or classify a system, and use det or inverse when the goal is a single square-matrix scalar or matrix result.
Frequently asked questions
How do I find a determinant?
Select a square matrix, edit its cells, and press det. A 2×2 example [[1,2],[3,4]] returns -2.
How do I find a matrix inverse?
Press A^-1 on a square invertible matrix. Singular matrices report no inverse instead of a numeric soup.
Why can't I multiply these matrices?
Matrix multiply needs the column count of A to equal the row count of B. The calculator checks that before multiplying and shows a dimension error when it fails.
What does rref do?
rref reduces the active matrix to reduced row echelon form, which is the standard form used to read solutions of linear systems.
What is a singular matrix?
A singular matrix has determinant zero and no inverse. The Matrix Calculator detects that during inversion and states no inverse.
Is the matrix calculator free?
Yes. The Matrix Calculator is free to use on Quick Calculators.
Summary
The Matrix Calculator covers the linear algebra operations most homework and lab workflows need: det, inverse, transpose, multiply, add, rref, trace, and square. It stays separate from static matrix pages in Math Calculators while linking across for readers who want both an instrument and a worked formula page.