Is Every Statement About Matrix Squares True?

[tysonk]

Can someone verify these for me and explain?
True/False
No square matrix with real entries can obey A^2 = -I
The only 2X2 matrix that obeys A^2 = 0 is A=0
The only 2X2 matrices that obey A^2=A are A=0 and A=I

Much appreciated.

 

[lurflurf]

Do you think they are true or false?

 

[tysonk]

Intuitively,
-false
-false
-true

 

[lurflurf]

What about A^2 when A={{1,0},{0,0}}?
You can show a statement is false with one example.
Can you find counter examples for the first 2?