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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Matrices

NDA 2017 · Mathematics · Matrices

If A is a square matrix, then the value of adj A^T-(adj A)^T is...

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

Options

  1. AA
  2. B2∣A∣I2|\mathrm{ A}| \mathrm{I}, where I is the identity matrix
  3. Cnull matrix whose order is same as that of A
  4. Dunit matrix whose order is same as that of A

Correct answer

C. null matrix whose order is same as that of A

Step-by-step solution

We know, Adj⁡AT=(adj⁡A)T∴adj⁡AT−(adj⁡A)T=adj⁡AT−adj⁡AT=0\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.
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