$2.$ Determine for the following code how many pages are transferred between disk and main memory, assuming each page has $512$ words, the active memory set size is $512($i$.$ e$.,$ at any time no more than $512$ pages may be in main memory$),$ and the replacement strategy is LRU $($the Least Recently Used page is always replaced$)$; also assume that all two$-$dimensional arrays are of size $(\backslash (1$: $1024,1$: $1024\backslash ))$ and each array element occupies one word,

$```$

for I :$=1$ to $1024$ do

for J :$=1$ to $1024$ do

$\{$A$[$I$,$J$]$:$=$A$[$J$,$I$]*$B$\{$J$,$I$]\}$

$```$

provided the arrays are mapped into the main memory space in column$-$major order,