How many skew-symmetric matrices of order 3 × 3 can be formed if each element is −1, 0 or 1?

9

Correct answerYour answer

26

Correct answerYour answer

27

Correct answerYour answer

729

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Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

The diagonal must be 0, and each element below the diagonal is fixed by the one above it, $a_{ji} = -a_{ij}$ .
So only the 3 places above the diagonal are free, each with 3 choices: $3^3 = 27$ . Every negative is again −1, 0 or 1.

Worth noting

729 is $3^6$ : it fills the places below the diagonal freely too, when they are fixed by those above.

Ten questions from Matrices, at your own pace.

Explanation