Question

If is an orthogonal matrix prove that moduls of a =1

Answer 1

   If number of rows is odd and det(A)=+1 (for orthogonal matrices this value is +1 or -1) then with the following trick:

det(A-1 * E)=det(A-E)=det(A’-E’)=det(A) * det(A’-E) = det(AA’-AE)=det(E-A)=(-1)^n det(A-E) => (1–(-1)^n)det(A-E)=0

You can be sure that real value +1 is eigenvalue

Step-by-step explanation:

Answer 2

Step-by-step explanation:

The second statement should say that the determinant of an orthogonal matrix is ±1 and not the eigenvalues themselves. R is an orthogonal matrix, but its eigenvalues are e±i. The eigenvalues of an orthogonal matrix needs to have modulus one. If the eigenvalues happen to be real, then they are forced to be ±1.