If $(A-I)^2=0$ than it minimal polynomial divides $(A-I)^2=0$, so $M\_A=(A-I)$ or $M\_A=(A-I)^2$. If $M\_A=A-I$ than $A=I$, and if $M\_A=(A-I)^2$ than A is similar to $$D=\operatorname{diag}(J\_2(1),J\_1(1),...,J\_1(1))$$ 

But I cannot find any example of orthogonal matrix that it minimal polynomial is $M\_A=(A-I)^2$. Does that matrix exists ?

Thanks.