# Transpose of Transpose of Matrix

## 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.

$\blacksquare$