For a 3 3 matrix M , let trace (M) denote the sum of all the diagonal elements of M . Let A be a 3 3 matrix such that |A|= 1 2 and trace (A)=3 . If B= adj ( adj (2 A)) , then the value of |B|+ trace (B) equals :

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Quantrex Academy · Accepted Answer

Correct answer: D. 280

tr (A)=3 and |A|= 1 2 Now, B= adj ( adj (2 A))=|2 A|³⁻² (2 A)=2^3|A| 2 A=8 A aligned & tr (B)=8 tr (A)=24 & and |B|=|8 A|=8^3 1 2 =256 & trace (B)+|B|=24+256 aligned =280

For a 3 3 matrix M , let trace (M) denote the sum of all the diagonal elements of M . Let A be a 3 3 matrix such that |A|= 1 2 and trace (A)=3 . If B= adj ( adj (2 A)) , then the value of |B|+ trace (B) equals :

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