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Let M be a square matrix of order 3 whose elements are real numbers and a d j a d j M = 36 0 - 4 0 6 0 0 3 6 , then the absolute value of T r M is [Here, a d j P denotes adjoint matrix of P and T r P denotes trace of matrix P i.e. sum of all principal diagonal elements of matrix P ]

Correct answer

8

Step-by-step solution

a d j a d j M = M n - 2 M ∴ order of M is 3 a d j a d j M = M M = 36 0 - 4 0 6 0 0 6 6 Taking determinant on both the sides M 4 = 36 0 - 4 0 6 0 0 3 6 M 4 = 6 4 ⇒ M = ± 6 hence, M = ± 6 0 ± 2 3 0 ± 1 0 0 ± 1 2 ± 1 T r   M = 8

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