Matrix Calculator
Perform determinants, inverse, transpose, addition, and matrix multiplication in a visual grid.
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Matrix Formulas & Calculation Methods
View All Math Formulas Handbook →Determinant Formula ($2 \times 2$)
Cross-multiplication of diagonals.
$$ \det(A) = \begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc $$
Matrix Inverse Formula ($2 \times 2$)
Adjugate divided by determinant.
$$ A^{-1} = \frac{1}{ad - bc} \begin{pmatrix} d & -b \\ -c & a \end{pmatrix} $$
Matrix Multiplication ($C = AB$)
Dot product of row $i$ from $A$ and column $j$ from $B$.
$$ C_{ij} = \sum_{k=1}^{p} A_{ik} B_{kj} = A_{i1}B_{1j} + A_{i2}B_{2j} + \dots + A_{ip}B_{pj} $$