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If the system of equations x=cy+bz,y=az+cx,z=bx+ay  has a nonzero solution then  a2+b2+c2+2abc=

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Correct option is B

x=cy+bz,y=az+cx,z=bx+ay⇒−1cbc−1aba−1xyz=000 Given equations has non zero solution ⇒−1cbc−1aba−1=0⇒−11−a2−c(−1−ab)+b(ac+b)=0⇒−1+a2+c2+abc+abc+b2=0⇒a2+b2+c2+2abc=1


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If the system of equations, ax+by+cz=0 , bx+cy+az=0  and cx+ay+bz=0  have non trivial solution, then


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