The matrices
\(A= \binom{1 \text{ }x}{y \text{ }1} \)
\(B = \binom{-1 \text{ } x}{y \text{ }-1}\)
are inverses
what is xy?
Because these are inverses AB = the identity matrix
[ 1 x ] * [ - 1 x ] = [ 1 0 ]
[ y 1 ] [ y - 1 ] [ 0 1 ]
So....by matrix multiplication, we have
[ - 1 +xy x - x ] = [ 1 0 ]
[ -y + y xy -1 ] [ 0 1 ]
Which implies that
xy - 1 = 1 add 1 to both sides
xy = 2