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Step-by-Step Solution
About the Matrix Calculator
The Matrix Calculator performs all standard matrix operations including addition, subtraction, multiplication, determinant, inverse, transpose, eigenvalues, and eigenvectors — all shown step by step.
Key Formulas
Determinant 2×2
|A| = ad − bc
Inverse 2×2
A⁻¹ = (1/|A|)·[[d,−b],[−c,a]]
Matrix Multiply
C[i,j] = Σ A[i,k]·B[k,j]
Transpose
(Aᵀ)[i,j] = A[j,i]
Eigenvalue
det(A − λI) = 0
Trace
tr(A) = Σ Aᵢᵢ