Check whether a square matrix is its own inverse — A × A equals the identity matrix.
How It Works
How Involutory Matrix Checker Works
The calculator multiplies the matrix by itself and checks whether the result is exactly the identity matrix — if so, applying the matrix twice undoes itself completely, meaning the matrix is its own inverse.
Worked Example
See It In Action
The matrix with rows 1,0 / 0,-1 (a reflection) squares to the identity matrix, so it's involutory.
FAQ
Frequently Asked Questions
What kind of transformations are involutory?
Reflections are the classic example — reflecting a point across a line or plane twice returns it to its original position, which is exactly what makes the corresponding matrix involutory.
Is the identity matrix itself involutory?
Yes — the identity matrix squared is still the identity matrix, so it trivially satisfies the condition.
