Similar to symmetric matrix?

Algebra Level 2

Given that $A$ is a $2017\times2017$ matrix and $a_{mn}$ denotes the entry in the $m$ th row and $n$ th column in $A$ . If $a_{mn} = -a_{nm} = mn$ , find $|A^{2017}|$ .

The answer is 0.

1 solution

Tommy Li
Oct 2, 2017

$A = -A^T$

$|A^{2017}| = (-1)^{2017} |A^{2017}|$

$2|A^{2017}| = 0$

$|A^{2017}| = 0$

How can this matrix exist though? Consider the entry $a_{11}$ . Surely, $a_{11} = -a_{11} = 1$ which is impossible.

Joe Mansley - 3 years ago

Similar to symmetric matrix?

The answer is 0.

1 solution

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