Question

Please show that (I - 2A) equals its own inverse if A is indempotent--matrices

Answer 1

\[
MM^{-1}=I
\]So you need to show \[
(I-2A)(I-2A)=I
\]

Answer 2

\[
\begin{split}
(I−2A)(I−2A)
&=I(I−2A)−2A(I−2A)\\
&=II-2A-2A+(-2A)(-2A)\\
&=I-4A+4(AA) \\
&= I-4A+4A\\
&=I
\end{split}
\]

Answer 3

Medals. All of them.

Answer 4

thankx