We consider the array $\backslash \backslash ($ B $\backslash \backslash )$ as follows: suppose the row $\backslash \backslash ($ i $\backslash \backslash )$ of $\backslash \backslash ($ A $\backslash \backslash )$ is in the form $\backslash \backslash (($a$\_\{$i$1\},$ a$\_\{$i$2\},\backslash$ldots$,$ a$\_\{$i$($t$+2)\})\backslash \backslash )$ and the row $\backslash \backslash ($ j $\backslash \backslash )$ of $\backslash \backslash ($ A$\text{'}\backslash \backslash )$ is in the form $\backslash \backslash (($a$\text{'}\_\{$j$1\},$ a$\text{'}\_\{$j$2\},\backslash$ldots$,$ a$\text{'}\_\{$j$($t$+2)\})\backslash \backslash ).$ Then, we set the row $\backslash \backslash ($ B$\_\{($i$,$j$)\}\backslash \backslash )$ as follows:

$\backslash \backslash [$

$(($a$\_\{$i$1\},$ a$\text{'}\_\{$j$1\}),($a$\_\{$i$2\},$ a$\text{'}\_\{$j$2\}),\backslash$ldots$,($a$\_\{$i$($t$+2)\},$ a$\text{'}\_\{$j$($t$+2)\}))$

$\backslash \backslash ]$

The array $\backslash \backslash ($ B $\backslash \backslash )$ has dimensions $\backslash \backslash (($n$^2$ n$\text{'})\backslash$times $($t$+2)\backslash \backslash )$ and its members are from the set $\backslash \backslash (\backslash \{(1,1),(1,2),\backslash$ldots$,($n$,$n$\text{'})\backslash \}\backslash \backslash ).$ Prove The constructed array $\backslash \backslash ($ B $\backslash \backslash )$ is a reliable arrangement and generates the desired Latin double square.