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NDA 2016 Maths · Mathematics · Matrices · easy

For A=beginpmatrix2&3\\1&4endpmatrix, the element in the first row and second column of adjA is

Single correct option

For A=(2314)A=\begin{pmatrix}2&3\\1&4\end{pmatrix}, the element in the first row and second column of adj⁡A\operatorname{adj}A is
  1. A. 33
  2. B. −1-1
  3. C. 44
  4. D. −3-3
Show answer and solution

Answer: (D) −3-3

For a 2×22\times2 matrix, the adjoint is obtained by swapping the diagonal entries and changing the signs of the off-diagonal entries: adj⁡A=(4−3−12)\operatorname{adj}A=\begin{pmatrix}4&-3\\-1&2\end{pmatrix}. The required element is −3-3. Taking the entry 33 without changing its sign is the common slip.
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Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake