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NDA 2023 Maths · Mathematics · Matrices · medium

If A=beginpmatrix4&3\\3&2endpmatrix, the sum of the diagonal entries of A^-1 is

Single correct option

If A=(4332)A=\begin{pmatrix}4&3\\3&2\end{pmatrix}, the sum of the diagonal entries of A−1A^{-1} is
  1. A. 66
  2. B. −6-6
  3. C. −1-1
  4. D. 11
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Answer: (B) −6-6

det⁡A=8−9=−1\det A=8-9=-1, so A−1=1−1(2−3−34)=(−233−4)A^{-1}=\dfrac1{-1}\begin{pmatrix}2&-3\\-3&4\end{pmatrix}=\begin{pmatrix}-2&3\\3&-4\end{pmatrix} and the trace is −2−4=−6-2-4=-6. Forgetting the factor 1det⁡A=−1\dfrac1{\det A}=-1 gives +6+6, and −1-1 is the determinant itself.
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Original question written in the NDA 2023 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