Matrices P and Q are defined by P=[tex]\left[\begin{array}{ccc}x&2\\-5&-1\\\end{array}\right][/tex] and Q=[tex]\left[\begin{array}{ccc}2&-3\\4&y\\\end{array}\right][/tex]. Where x,y∈R

(a) Given the determinant of P is 2, obtain:

(i) The value of x.

(ii) [tex]P^{-1}[/tex]

(iii) [tex]P^{-1}Q'^{-1}[/tex], where Q' is the transpose of Q.

(b) The matrix R is defined by R=[tex]\left[\begin{array}{ccc}5&-2\\z&-6\\\end{array}\right][/tex], where z∈R.

Determine the value of z such that R is singular.