if 3x3 matrix A=[a b c b c a c a b] where a,b,c are positive real numbers such that abc= 1 and A'A=I then find the value of a^3+b^3+c^3

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Please find below the solution to the asked query:

Given A=abcbcacababcbcacab×abcbcacab=100010001a2+b2+c2ab+bc+caac+bc+abab+bc+caa2+b2+c2ac+bc+abac+bc+abac+bc+aba2+b2+c2=100010001so,a2+b2+c2=1ab+bc+ca=0so,a+b+c2=a2+b2+c2+2ab+bc+ca=1+0=1so,a+b+c=1now,we know that,a3+b3+c3-3abc=a+b+ca2+b2+c2-ab-bc-cagiven abc=1.a3+b3+c3-3=1.0-0a3+b3+c3=3

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