SOLUTION: a square matrix A is said to be idempotent A^2=A (a)give an example of idempotent matrix other than 0 and I (b)show that,if matrix A is both idempotent and invertible then A=I

Question 1062852: a square matrix A is said to be idempotent A^2=A
(a)give an example of idempotent matrix other than 0 and I
(b)show that,if matrix A is both idempotent and invertible then A=I
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!

Just the (a) part:

Let A = 

be idempotent.  Then

   

 





So we set each elements on the left equal to the corresponding
element on the right:



Divide the second one through by x or the third one through
by y:

w + z = 1 

So we pick, say w = 1/4 and z = 3/4 since they have sum 1 

Substituting in








 
 

Choose x=1 and y=3/16, because their product is 3/16.

Substitute in

A = 

A = 

Edwin

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