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NDA 2020 Maths · Mathematics · Matrices · medium

The sum of all the elements of the inverse of the matrix beginbmatrix2&1\\5&3endbmatrix is

Single correct option

The sum of all the elements of the inverse of the matrix [2153]\begin{bmatrix}2&1\\5&3\end{bmatrix} is
  1. A. 1
  2. B. −1-1
  3. C. 0
  4. D. −2-2
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Answer: (B) −1-1

The determinant is 6−5=16-5=1, so the inverse is [3−1−52]\begin{bmatrix}3&-1\\-5&2\end{bmatrix} (swap the diagonal, change the signs of the off-diagonal). The sum is 3−1−5+2=−13-1-5+2=-1. Not changing signs gives sum 11.
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Original question written in the NDA 2020 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