Let A=02bcab-ca-bc be an orthogonal matrix then the values of a, b, c are

A=02bcab-ca-bcand A'=0aa2bb-bc-ccAs A is orthogonal∴ AA′ = I⇒02bcab-ca-bc0aa2bb-bc-cc=100010001⇒4b2+c22b2-c2-2b2+c22b2-c2a2+b2+c2a2-b2-c2-2b2+c2a2-b2-c2a2+b2+c2 =100010001∴ Using definition of equality of two matrices4b2+c2=1,2b2-c2=0,a2+b2+c2=1On solving them,a=±12,b=±16,c=+13