Only two determinant calculation had left!

I can't prove even one of them! I am been trying all the week, but I failed!

1. The diagonal is "a" and all the rest is "b"

a , b, ... , b

b , a,

.

.

.

b , ... , a

2. Matrix in which the diagonal is "0". Above the diagonal is "-1" and "1" is below the diagonal. (Need to separate to 2 cases when n is odd and when n is even)

0,-1,...,-1

1,0

.

.

.

1,... 0

I know that when n is odd so det=0 and when n is even so det=1, but how to prove it ?!

Thank you very much!