$(2$ points$)$ In a typical first$-$year linear algebra course, a commonly$-$taught method for finding the inverse of a square matrix

is to put

into reduced$-$row echelon form $($RREF$).$ If the result is of the form

$,$ then

is the inverse of

$.$ We will see that this method is rather slow compared to the inv function in MATLAB.

We can show the elapsed time by enclosing our command between tic and toc. For example, A $=$ rand$(500)$; tic; inv$($A$)$; toc; will show the elapsed time for computing the inverse of the random matrix A$.$

In MATLAB, define a

matrix

so that all the diagonal entries are equal to $5$ and the remaining entries are all equal to

$.$

Write code to obtain the elapsed time for computing inv$($A$),$ the elapsed time for computing the RREF of

$,$ and the elapsed time for computing an LU$-$decomposition of

$.$ In a comment after the code for this question, report your observations.