Matrix Calculator
Enter a 2×2 or 3×3 matrix below to add, subtract, multiply, or find a determinant — plus the inverse for 2×2 matrices.
Matrix Multiplication
Each result entry is a dot product: multiply matching row/column entries and add them up.
Worked example
A = [[1, 2], [3, 4]], B = [[5, 6], [7, 8]].
Top-left entry: (1×5) + (2×7) = 5 + 14 = 19
A × B = [[19, 22], [43, 50]]
Keep going
- Matrix operations like the determinant and inverse are one way to solve a 2x2 system; the system of equations calculator solves that same system directly by substitution. System of Equations Calculator
- Cross product uses a determinant-style calculation similar to a 2x2 or 3x3 matrix; the cross product calculator applies that same determinant logic to two 3D vectors. Cross Product Calculator
Frequently Asked Questions
How do you multiply two matrices?
Each entry in the result is the dot product of a row from the first matrix and a column from the second: row i, column j of the result is the sum of (row i of A) × (column j of B), entry by entry.
How do you find the determinant of a 2×2 matrix?
For [[a, b], [c, d]], the determinant is a×d − b×c.
How do you find the inverse of a 2×2 matrix?
Swap the diagonal entries, negate the other two, then divide every entry by the determinant: for [[a, b], [c, d]] with determinant ad − bc, the inverse is [[d, −b], [−c, a]] ÷ (ad − bc). A matrix with a determinant of 0 has no inverse.
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