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Match the following Column I and Column ...

Match the following Column I and Column II

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The correct Answer is:
A, B, C
(A) det `(6A^(-1))= 6^(3) det (A^(-1))=216/(det (A) ) = 216/3 = 72`
(B) `det [adj (adj (2A))] = [ det (2A)]^(4) = [2^(3) det (A) ]^(4)`
`= 2^(12) [det (A) ]^(4)`
`=2^(12) (1/4)^(4) = 2^(4) = 16`
(C ) `because (A+B)^2 = A^(2) + AB + BA + B^(2) `
`rArr A^(2) + B^(2) = A^(2) + AB + BA+ B^(2) `
`[because (A+B)^(2) = A^(2) +B^(2)]`
`rArr AB+BA = O rArr AB = - BA`
`therefore det (AB) = det (-BA) = -det (BA) `
`rArr det (A) cdot det(B) = - det B cdot det (A)`
`rArr 2 det (A) cdot det(B) = 0 rArr 4 det (B) = 0 [ because det (A) = 2] `
`therefore det (B) = 0`
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