DeterminantHard
Question
Let M be a 3 × 3 non-singular matrix with det(M) = α. If M-1 adj(adj M) = kI, then the value of ′k′ is :
Options
A.1
B.α
C.α2
D.α3
Solution
M-1 adj(adj M) = kI
Pre-multiplying by M
adj(adj M) = kM
det(adj(adj M)) = det(kM)
(det M)(3 - 1)2 = k3 det (M)
(det M)4 = k3 (det M)
(det M)3 = k3
det M = k ⇒ k = α
Pre-multiplying by M
adj(adj M) = kM
det(adj(adj M)) = det(kM)
(det M)(3 - 1)2 = k3 det (M)
(det M)4 = k3 (det M)
(det M)3 = k3
det M = k ⇒ k = α
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