Let A= [ array lll a & b & c b & c & a c & a & b array ] and B= [ array lll b c-a^2 & c a-b^2 & a b-c^2 c a-b^2 & a b-c^2 & b c-a^2 a b-c^2 & b c-a^2 & a c-b^2 array ] be two non-singular matrices such that (A^2-2 I ) B=O where abc0 , th

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Let A= [ array lll a & b & c b & c & a c & a & b array ] and B= [ array lll b c-a^2 & c a-b^2 & a b-c^2 c a-b^2 & a b-c^2 & b c-a^2 a b-c^2 & b c-a^2 & a c-b^2 array ] be two non-singular matrices such that (A^2-2 I ) B=O where a>b>c>0 , then which of the following statement(s) is(are) correct? [Note: I is an identity matrix of order 3 and T r .(P) and det. (P) denote trace and value of the determinant of square matr

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Correct answer: D. det (A- 2 B)=-54 2

aligned & (A^2-2 I ) B=0 A^2=2 I and B=a d j A=|A| A 2 =- 2 A |A|=-2 2 & A B=A( adj A)=|A| I & tr. (A B)=3|A|=-6 2 & and det (A- 2 B)= det (A+2 A)= det (3 A)=27(-2 2 )=-54 2 aligned

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