If $A = \begin{bmatrix}1 & -2 & 3 \\ 0 & 4 & 5\end{bmatrix}$, what is $A'$?

Explanation

1. 01

   The transpose turns each row into a column, in order: row 1 becomes column 1.

2. 02

   So $A' = \begin{bmatrix}1 & 0 \\ -2 & 4 \\ 3 & 5\end{bmatrix}$, of order 3 × 2.