$[10$ pts$]$ Matrix transpose: Given a matrix A of size $n{n}_{?},$ the transpose of $A$ is the matrix $A^T$ created

by writing the rows of $A$ as the columns of $A^T.$ See the example below.

$A=\left[\begin{array}{cccc}{a}_{1,1}& a_{1,2}& a_{1,3}& a_{1,4}\\ a_{2,1}& a_{2,2}& a_{2,3}& a_{2,4}\\ a_{3,1}& a_{3,2}& a_{3,3}& a_{3,4}\\ a_{4,1}& a_{4,2}& a_{4,3}& a_{4,4}\end{array}\right],$ then $A^T=\left[\begin{array}{cccc}{a}_{1,1}& a_{2,1}& a_{3,1}& a_{4,1}\\ a_{1,2}& a_{2,2}& a_{3,2}& a_{4,2}\\ a_{1,3}& a_{2,3}& a_{3,3}& a_{4,3}\\ a_{1,4}& a_{2,4}& a_{3,4}& a_{4,4}\end{array}\right].$

First design a sequential algorithm for find the transpose. Then design a parallel algorithm to find

the transpose of a matrix for an EREW PRAM model with $O(n^2)$ processors. Provide pseudocode

and analysis.