Consider the matrix A=(abcd)A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}A=(acbd). What is the condition for AAA to be orthogonal?
a2+c2=1,b2+d2=1,ab+cd=0a^2+c^2=1, b^2+d^2=1, ab+cd=0a2+c2=1,b2+d2=1,ab+cd=0
a2+b2=1,c2+d2=1,ac+bd=0a^2+b^2=1, c^2+d^2=1, ac+bd=0a2+b2=1,c2+d2=1,ac+bd=0
ad−bc=1ad-bc=1ad−bc=1
a=d,b=−ca=d, b=-ca=d,b=−c