Perform matrix operations for 2×2 and 3×3 matrices — addition, subtraction, multiplication, scalar multiply, determinant, inverse, and transpose — with full step-by-step working.
Matrix Setup
Matrix A
Matrix B
Result
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RESULT MATRIX
Select an operation and fill in the matrix values
Supports 2×2 and 3×3 matrices for all standard operations.
Frequently Asked Questions
When does a matrix have an inverse?
A matrix is invertible (non-singular) if and only if its determinant is non-zero. If det(A) = 0, the matrix is singular and has no inverse. For 2×2, A⁻¹ = (1/det) × [[d, -b], [-c, a]].
How is matrix multiplication different from scalar multiplication?
Scalar multiplication multiplies every element by a constant k. Matrix multiplication (A×B) is a dot product: each result element (i,j) is the sum of the products of row i of A with column j of B. Note: A×B ≠ B×A in general.