Transpose of Transpose of Matrix

Theorem
Let $$\mathbf{A}$$ be a matrix.

Let $$\mathbf{A}^t$$ be the transpose of $$\mathbf{A}$$.

Then $$\left({\mathbf{A}^t}\right)^t = \mathbf{A}$$.

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