JEE Main 2020MathematicsMatricesHardNumerical

JEE Main 2020 — Matrices Question with Solution

JEE Main 2020 (08 Jan Shift 1)

Question

The number of all 3×3 matrices A, with entries from the set -1,0,1 such that the sum of the diagonal elements of AAT is 3, is ___________.

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Show full solutionCorrect answer: 672
Correct answer
672

Step-by-step explanation

Let, A=aii3×3
tr(AAT)=3
a112+a122+a132+a212+.......+a332=3
Possible cases
0,0,0,0,0,0,1,1,1→10,0,0,0,0,0,-1,-1,-1→10,0,0,0,0,0,1,1,-1→30,0,0,0,0,0,-1,1,-1→3 9C6×8=84×8=672

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About this question

This is a previous-year question from JEE Main 2020, covering the Matrices chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.