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]]
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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