i found this question that is made out of 2 claims and i've got to deicde if both wrong,correct or just one right. one of them i think i succeed solving, but i've had hard time with the other one for hours.
1)in $M _{nxn}^R, n>1, exists an non-zero symmetrical matrice that is orthogonal to every diagonal matrice.
2)let U be a subspace of $R^n$ that is defined as $U={(x_1,..,x_n) \in R^n | \sum _{i=1} ^n x_i=0}$ then the vector {(1,1,1,...,1) is a basis for $U^\bot$
i don't know how to solve the first one at all. regarding the second claim, it is true since an orthogonal basis can be made if $<v_i,v_j>$=1 if i=j and 0 if $i\neq j$, so {(1,1,1,..,1)} can be a basis for $U^\bot$.
thank you for helping me.