Matrix Calculator

Perform matrix operations: addition, subtraction, multiplication, determinant, and transpose for 2x2 matrices.

Operation

Matrix A [1,1]

Matrix A [1,2]

Matrix A [2,1]

Matrix A [2,2]

Tab to move between fields

Result [1,1]

Result [1,2]8

Result [2,1]10

Result [2,2]12

Determinant of A0

Trace of A5

How to Use This Calculator

Enter the four elements of Matrix A (a11, a12, a21, a22) and Matrix B row by row.
Select the operation: addition, subtraction, and multiplication follow standard linear algebra rules.
Determinant of a 2×2 matrix: det(A) = a11×a22 − a12×a21; a non-zero determinant means the matrix is invertible.
Transpose swaps rows and columns; Trace is the sum of diagonal elements (a11 + a22).
The inverse A⁻¹ is computed when det(A) ≠ 0: A⁻¹ = (1/det) × [[a22, -a12], [-a21, a11]].
Matrix multiplication is not commutative — A×B and B×A generally give different results.

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Formula

For 2x2 matrices: det(A) = a₁₁a₂₂ - a₁₂a₂₁

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