Given: p = \(\begin{pmatrix} m + 1 & m - 1 \\ m + 4 & m - 8 \end{pmatrix}\) and |p| = -32,

But the determinant of p = -32

[{(m + 1)(m - 8)} - {(m - 1)(m + 4)}] = - 34

[m\(^2\) - 8m + m - 8)] - [( m\(^2\) + 4m - m - 4] = - 34

[m\(^2\) - 7m - 8] - [m\(^2\) + 3m - 4] = -34

m\(^2\) - 7m - 8 - m\(^2\) - 3m + 4 = - 34

- 7m - 3m - 4 = - 34

- 10m = - 34 + 4 = - 30

m = \(\frac{-30}{-10}\) = 3

Hence, m = 3