Matrix calculator
Enter a matrix to find its determinant, inverse, transpose, rank, or a product with a second matrix.
Blank cells count as 0. You can type fractions such as 1/2.
What each operation does
The determinant is a single number that tells you whether a square matrix can be inverted. A zero determinant means the rows are dependent and no inverse exists. The inverse is the matrix that multiplies with the original to give the identity matrix. The transpose swaps rows and columns.
Adding and multiplying
You can only add or subtract matrices of the same size, and the operation works entry by entry. Multiplication is different: the number of columns in A must match the number of rows in B. The product has A’s rows and B’s columns, and order matters, so A × B is usually not the same as B × A.
Rank
The rank counts how many rows are independent of each other. A square matrix of size n is invertible exactly when its rank is n. Rank also tells you how many solutions a linear system has.
Fractions
Tick the fraction box to see answers like 3/4 instead of 0.75. Fractions are found by approximating each decimal, so for unusual values the tool falls back to decimals.