Q.Write the transpose of the matrix $\begin{pmatrix} 7 & 8 & -1 \\ 5 & 2 & 6 \\ 1 & 3 & 4 \end{pmatrix}$.

Write each row of the matrix as a column: $A^{T}=\begin{pmatrix} 7 & 5 & 1 \\ 8 & 2 & 3 \\ -1 & 6 & 4 \end{pmatrix}$. The transpose $A^{T}$ is formed by turning the rows of $A$ into columns (element $a_{ij}$ moves to position $ji$). Rows of $A$: $(7,8,-1)$, $(5,2,6)$, $(1,3,4)$ become the columns of $A^{T}$: $A^{T}=\begin{pmatrix} 7 & 5 & 1 \\ 8 & 2 & 3 \\ -1 & 6 & 4 \end{pmatrix}.$ …