Matrix Calculator
Perform various matrix operations including addition, multiplication, determinant, and more.
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Matrix Operations
Add or subtract corresponding elements:
\[ (A \pm B)_{ij} = A_{ij} \pm B_{ij} \]
Matrix multiplication:
\[ (AB)_{ij} = \sum_{k=1}^{n} A_{ik}B_{kj} \]
Scalar multiplication:
\[ (cA)_{ij} = cA_{ij} \]
2×2 matrix:
\[ \det\begin{pmatrix} a & b \\ c & d \end{pmatrix} = ad - bc \]
3×3 matrix:
\[ \det\begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix} = a(ei-fh) - b(di-fg) + c(dh-eg) \]
2×2 matrix:
\[ A^{-1} = \frac{1}{ad-bc}\begin{pmatrix} d & -b \\ -c & a \end{pmatrix} \]
For larger matrices, use the adjugate method or row operations.