Concept:For a 2×2 matrix (acbd), the determinant is ad−bc.We use the given determinant value to form and solve an equation in m.Explanation:The given matrix is p=(m+1m+4m−1m−8).So, ∣p∣=(m+1)(m−8)−(m−1)(m+4).Expand each product carefully.(m+1)(m−8)=m2−8m+m−8=m2−7m−8.(m−1)(m+4)=m2+4m−m−4=m2+3m−4.Thus, ∣p∣=(m2−7m−8)−(m2+3m−4).Simplify: ∣p∣=m2−7m−8−m2−3m+4.This gives ∣p∣=−10m−4.We are given ∣p∣=−34.Therefore, −10m−4=−34.Add 4 to both sides to get −10m=−30.Divide both sides by −10: m=−10−30=3.Answer:The value of m is 3.The correct option is C.