Q164 / 270 · NDA 2017 (Phase 2) · Mathematics

If $A$ is a square matrix, then the value of $\operatorname{adj} A^T-(\operatorname{adj} A)^T$ is equal to

  • A
    A
  • B
    $2|\mathrm{~A}| \mathrm{I}$, where I is the identity matrix
  • Correct answer
    C
    null matrix whose order is same as that of A
  • D
    unit matrix whose order is same as that of A

Solution

We know, $\operatorname{Adj} A^{\mathrm{T}}=(\operatorname{adj} A)^{\mathrm{T}}$ $\therefore \operatorname{adj} \mathrm{A}^{\mathrm{T}}-(\operatorname{adj} \mathrm{A})^{\mathrm{T}}=\operatorname{adj} \mathrm{A}^{\mathrm{T}}-\operatorname{adj} \mathrm{A}^{\mathrm{T}}=0$.

Hence, the correct answer is option: 'C'.

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