bantu in kak.......

det P = 2(3)- 1(5)
det P = 1

det Q = 5(1) - 1(4)
det Q = 1

det P⁻¹. Q⁻¹ =  det P x det Q = 1

[tex]P=\left[\begin{array}{cc} 2 & 5\\ 1 & 3 \end{array}\right],\qquad Q=\left[\begin{array}{cc} 5 & 4\\ 1 & 1 \end{array}\right][/tex]

[tex]P^{-1}=\left[\begin{array}{cc} 3 & -5\\ -1 & 2 \end{array}\right],\qquad Q^{-1}=\left[\begin{array}{cc} 1 & -4\\ -1 & 5 \end{array}\right][/tex]

[tex]P^{-1}Q^{-1}=\left[\begin{array}{cc} 8 & -37\\ -3 & 14 \end{array}\right][/tex]

[tex]\det\left(P^{-1}Q^{-1}\right)=8\left(14\right)-\left(-37\right)\left(-3\right)=1[/tex]