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Let M and N are two non singular matrices of order 3 with real entries such that a d j M = 2 N and a d j N = M . If M N = λ Ι , then the value of λ is equal to (where, a d j X represents the adjoint matrix of matrix X and I represents an identity matrix)

Correct answer

2

Step-by-step solution

a d j M = 2 N ⇒ a d j M = 2 N ⇒ M 2 = 8 N …. 1 a d j N = M ⇒ a d j N = M ⇒ N 2 = M …. 2 From 1 and 2 , we get, N = 2 , M = 4 Now, M N = a d j N N = N Ι = 2 Ι ⇒ λ = 2

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