- #1

christang_1023

- 27

- 3

- Homework Statement
- A square matrix ##A## is said to be

• an involutory matrix if ##A^2 = I##,

• an idempotent if ##A^2 = A##.

Show that every involutory matrix can be expressed as a difference of two idempotents.

- Relevant Equations
- The involutory matrix can be decomposed to ##A=\frac{1}{2}(I+A)-\frac{1}{2}(I-A)##

I feel confused about proving the two terms are idempotents.