Question

A square matrix is said to be 'idempotent' if A^2 = A. Show that if A is idempotent then 2A-I is invertible and is its own inverse?

Answer 1

(2A -I)^2 = 4A^2 - 4A + I = I

Answer 2

Oh man that was so simple don't why I didn't think of that

Answer 3

but wait how do you know if its its own inverse?

Answer 4

An identity matrix is its own inverse right? Just making sure

Answer 5

he multiplied it with itself and got I

Answer 6

and yes the identity matrix is its own inverse

Answer 7

2A-I is invertible because it has inverse one.

Answer 8

Okay gotcha

Answer 9

sir joemath answer my question please