- #1
JosephR
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Homework Statement
A martix A is said to idempotent if A²=A prove the following:
a) If A is idempotent then I-A is also idempotent
b) If A is idempotent and invertible then A=I
c) If A is idempotent then I-2A is invertible.Find (I-2A)-1 in terms of A
d)Give an example of a 2x2 idempotent matrix A such that A is not the zero or the identity matrix
2. The attempt at a solution
a) A²=A then,(I-A)(I-A)=I-A ( prove it)
= I²-2A+A² and since A²=A then I-A=I-A
b) A²=A
A.A=A ~~> A-1.A.A=A-1.A ~>IA=I ~>A=I
c) I'm Stuck
d) i knew this part :P
so please any help on part c) i have an exam tomorow :)
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