Hello, I have problem with matrices. Can somebody help me, Please....

If P^2 = P and P^-1 exists, find the determinant P and show that (I+P)^2 = I + 7P

Results 1 to 2 of 2

- Sep 17th 2012, 07:22 PM #1

- Joined
- Sep 2012
- From
- NS
- Posts
- 12

- Sep 17th 2012, 11:06 PM #2

- Joined
- Sep 2012
- From
- Australia
- Posts
- 6,566
- Thanks
- 1708

## Re: Help me...

Hey AuXian.

Firstly, if you have square matrices A and B then det(AB) = det(A)det(B) and P has to be square so if P^2 = P then det(P^2) = det(P)det(P) = det(P) which means that det(P) = 1 or 0. But if P has an inverse it can't equal 0 so it has to be 1.

Now for the second example, what is your distributive rule when it comes to matrices (i.e what is (A+B)^2 if it equals (A+B)(A+B))?