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\text { 1. }\left(5 \text { points) If } n \in \mathbb{N} \text { and } A \in \mathbb{R}^{(2 n+1) \times(2 n+1)}, A^{T}=-A\right. \text { , } show that A

is not invertible. Hint: start by taking the determinant of both sides.

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