Q1: What is the transpose of the matrix $ A = \begin{pmatrix} 2 & 3 \ 4 & 5 \end{pmatrix} $.

A1: $$ A^T = \begin{pmatrix} 2 & 3 \ 4 & 5 \end{pmatrix} $$

A2: $$ A^T = \begin{pmatrix} 2 & 4 \ 3 & 5 \end{pmatrix} $$

A3: $$ A^T = \begin{pmatrix} 5 & 3 \ 4 & 2 \end{pmatrix} $$

A4: $$ A^T = \begin{pmatrix} 4 & 3 \ 2 & 5 \end{pmatrix} $$

Q2: Let $A$ be a matrix and $A^T$ be the transpose. In which case do we have $A = A^T$?

A1: We have this for square matrices that are symmetric.

A2: We have this for all matrices.

A3: We have this for square matricses.

A4: We have this for $A = \begin{pmatrix} 2 & 1 \ 0 & 0 \end{pmatrix} $

A5: It’s not possible to find matrices with this property.