Matrix Calculator

It works with square matrices from 2×2 to 4×4 and computes A + B, A − B, A × B, the determinant of A, the inverse of A, the transpose of A, and a scalar multiple of A. Enter the numbers in the grids, pick an operation, and the result appears instantly — everything runs in your browser.

By cofactor (Laplace) expansion. For a 2×2 matrix [[a,b],[c,d]] the determinant is ad − bc. For larger matrices it expands along the first row using minors and alternating signs. A determinant of zero means the matrix is singular and has no inverse.

Using Gauss–Jordan elimination: the matrix is augmented with the identity and row-reduced until the left side becomes the identity, leaving the inverse on the right. If the determinant is zero the matrix is not invertible, and the calculator says so instead of returning a result.

Matrix multiplication is not element-by-element. Each result entry is the dot product of a row of A with a column of B, so the number of columns in A must equal the number of rows in B. This calculator uses equal-size square matrices, so A × B is always defined — but note A × B usually does not equal B × A.

The transpose flips a matrix over its main diagonal, turning rows into columns: entry (i, j) becomes (j, i). It is used throughout linear algebra, for example in computing symmetric matrices, covariance, and least-squares solutions.