A square root of the zero matrix

Task number: 2423

Find a nonzero matrix \(\mathbf A\) such that \(\mathbf A\mathbf A=\mathbf 0\).

  • Hint

    Consider how rows could be eliminated by columns.

  • Result

    For instance, \(\mathbf A= \begin{pmatrix} 1 & 1 \\ -1 & -1 \\ \end{pmatrix} \).

Difficulty level: Easy task (using definitions and simple reasoning)
Proving or derivation task
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