if A and B are orthogonal matrices of same order such that det(A)+det(B)=0, find det(A+B).

Since, for the orthogonal matrices, the value of the determinant is either equal to 1 or -1. 

And since, here det(A) + det(B) = 0, hence we can assume that det(A) = 1 and then, det(B) = -1. 

 

Now assuming 2 examples of orthogonal 2 x2 matrices