Matrix Calculator
Perform matrix addition, subtraction, multiplication, find the determinant, inverse, and transpose of 2×2 and 3×3 matrices.
Matrix Operations Guide
Add / Subtract: Add or subtract corresponding elements. Matrices must be the same size.
Multiply: Each element of the result row×column is the dot product of the row from A and the column from B.
Determinant: A scalar value encoding matrix properties. For 2×2: det = ad − bc. Non-zero determinant means the matrix is invertible.
Inverse: A⁻¹ such that A × A⁻¹ = I (identity matrix). Only exists when det ≠ 0.
Transpose: Flip the matrix over its main diagonal — rows become columns.
Frequently Asked Questions
The determinant is a scalar value that encodes several properties of a matrix. For a 2×2 matrix [[a,b],[c,d]], det = ad − bc. A non-zero determinant means the matrix is invertible.
The inverse does not exist when the determinant equals zero. Such a matrix is called "singular" or "degenerate".
Matrix multiplication computes the dot product of rows and columns. It is not commutative (A × B ≠ B × A in general) and requires the number of columns in A to equal the number of rows in B.
The transpose of a matrix flips it over its main diagonal — rows become columns and columns become rows. For matrix A, the transpose is written Aᵀ.
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