Matrix Calculator — 2×2
Perform common 2×2 matrix operations with explicit entries and see whether matrix A is invertible.
Matrix A
Matrix B
det(A)-2
trace(A)5
A × B[[19, 22], [43, 50]]
A⁻¹[[-2, 1], [1.5, -0.5]]
How this tool works
For A=[[a,b],[c,d]], det(A)=ad−bc and A⁻¹=(1/det)[[d,−b],[−c,a]] when det is nonzero.
Example
Enter two small transformation matrices to multiply them and inspect the determinant of the first matrix.
Common questions
Why is the inverse unavailable when the determinant is zero?
A zero determinant means the linear transformation is singular, so no unique inverse matrix exists.
Does this support larger matrices?
This focused page handles 2×2 operations; larger matrix support can be added as a separate advanced utility.