$($Gaussian Elimination$)$

Given an $m-$by$-m$ nonsingular matrix $A,$ how do you efficiently solve the following problems, using Gaussian elimination with partial pivoting?

$($a$)$ Solve the linear system $A^{k}x=b,$ where $k$ is a positive integer.

$($b$)$ Compute $=c^T{A}^{-1}b.$

$($c$)$ Solve the matrix equation $Ax=B,$ where $B$ is $m-$by$-n.$

You should: $(1)$ describe your algorithms, $(2)$ present them in pseudocode $($using a Matlab$-$like language$),$ and $(3)$ give the required flops.