JEE Main 2022 · 27 Jul · Shift 1 · Mathematics Q28

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MathematicsInteger+4 / -1Question 28 of 90

Let S be the set containing all $3\times3$ matrices with entries from $\{-1,0,1\}$ . The total number of matrices $A\in S$ such that the sum of all the diagonal elements of $A^{\mathrm T}A$ is 6 is ______.

Your answer

Answer and worked solution

Official answer: 5376

Trace of $A^{\mathrm T}A$ is the sum of squares of all entries, so exactly six entries are $\pm1$ .

Count. $\binom96\cdot2^6=5376$ .

Answer: 5376

Topics:Special matrices Combinations

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JEE Main 2022 · 27 Jul · Shift 1, Mathematics question 28