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Let Z = 1 1 3 5 1 2 3 1 0 and P = 1 0 2 2 1 0 3 0 1 . If Z = P Q - 1 , where Q is a square matrix of order 3 , then the value of Tr a d j Q P is equal to (where Tr ( A ) represents the trace of a matrix A i.e. the sum of all the diagonal elements of the matrix A and adjB represents the adjoint matrix of matrix B )

Options

  1. A3
  2. B- 1
  3. C4
  4. D6 5

Correct answer

B. - 1

Step-by-step solution

Given, Z = PQ - 1 P = - 5 ,   Z = 10 Z = P Q ⇒ Q = - 5 10 = - 1 2 Z Q = P . a d j Q ⇒ P . a d j Q = - 1 2 Z Tr a d j Q . P = Tr P . a d j Q = - 1 2 Tr ( Z ) = - 1

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