Question: A and B are real nonzero 3 3 matrices and satisfy the equation 1. Prove that if B is orthogonal then A is antisymmetric.

A and B are real nonzero 3 × 3 matrices and satisfy the equation

(AB)T + B-A = 0

1. Prove that if B is orthogonal then A is antisymmetric.
2. Without assuming that B is orthogonal, prove that A is singular (i.e., its determinant
vanishes).

(AB)T + B-A = 0

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