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NDA 2018 Maths · Mathematics · Matrices · medium

What is the sum of the diagonal elements (trace) of the inverse of beginpmatrix2&1\\5&3endpmatrix?

Single correct option

What is the sum of the diagonal elements (trace) of the inverse of (2153)\begin{pmatrix}2&1\\5&3\end{pmatrix}?
  1. A. 1
  2. B. −5-5
  3. C. 5
  4. D. 3
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Answer: (C) 5

The determinant is 6−5=16-5=1. The inverse is 11(3−1−52)\frac11\begin{pmatrix}3&-1\\-5&2\end{pmatrix}, with trace 3+2=53+2=5. Remember to swap the diagonal entries and change the signs of the off-diagonal ones.
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Original question written in the NDA 2018 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