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Task number: 2424

Show that

  • Variant 1

    Matrix \(\mathbf A\mathbf A^T\) is always symmetric.

  • Variant 2

    Every matrix of type \(m \times n\) satisfies \(\mathbf I_m\mathbf A=\mathbf A=\mathbf A\mathbf I_n\).

  • Variant 3

    The product of regular matrices is regular.

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