GATE XE (Engineering Sciences) 2024 - Question 15

Section: Engineering Mathematics | Type: NAT | Marks: 1

Let 𝐴 be a 3 × 3 matrix whose eigenvalues are 2, 3, 4 and let 𝐼 be the identity matrix of order 3. If 𝐴−1 = 1 2𝑘(𝐴2 −9𝐴) + 13 𝑘𝐼 for some integer 𝑘≠0, then the value of 𝑘 is ______

Answer: 12