12 2 1 12. Show that A = 21-2 is orthogonal. 3 -22 -1 13. Show that the columns of a unitary matrix are orthogona 14. Show that the determinant of a unitary matrix is of ab det (AB) = det (A) det (B). 1 15. Show that A = = ( 2-4i 4i -4i 6 4i ) i -2-4i is unitary. 16. Show that the rows and columns of the unitary matrix in 1 1 1 0 1 1 0-1 -i 17. Show that A = 1 -1 0 is unitary. i 0 -i i 1