Transpose of Transpose of Matrix

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Theorem

Let $\mathbf A$ be a matrix.

Let $\mathbf A^\intercal$ be the transpose of $\mathbf A$.


Then:

$\paren {\mathbf A^\intercal}^\intercal = \mathbf A$


Proof

Follows directly from the definition of the transpose of a matrix.

$\blacksquare$


Sources