Question

Let M be a 3×3 non-singular matrix with det(M)=α. If |M⁴operatornameadj(M)|=K, then the value of K is

• A. \(1\)
• B. \(\alpha\)
• C. \(\alpha^2\)
• D. α³

Hint:

For an n× n matrix, |operatornameadj(A)|=|A|ⁿ-1.

Answer 1

The Correct Option is D

|M⁴operatornameadj(M)|=|M|⁴|operatornameadj(M)| For a 3×3 matrix, |operatornameadj(M)|=|M|² ⟹ K=α⁴·α²=α⁶ Thus, K=α³