Work with two matrices $A$ and $B$. Choose determinant, inverse (when it exists), or the products $AB$ / $BA$. Entries are ordinary numbers.
2×2 matrix toolkit
Matrix A
Matrix B
What it computes. $\det$, $A^{-1}$ via the adjugate formula, and ordinary matrix multiplication for $2\times 2$ arrays.
Limitations. Singular matrices have no inverse. Multiplication is not commutative — compare $AB$ and $BA$. See the disclaimer.
Related: Linear algebra · Determinant · Matrix · Eigenvalues (2×2)