Let M and N are two non singular matrices of order 3 with real entries such that adjM=2N and adjN=M. If MN=λΙ, then the value of λ is equal to (where…

Question

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

MARKS Content Team · Accepted Answer

Correct answer: 2. adjM=2N⇒adjM=2N⇒M^2=8N …. 1 adjN=M⇒adjN=M⇒N^2=M …. 2 From 1 and 2, we get, N=2,M=4 Now, MN=adjNN=NΙ=2Ι⇒λ=2

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)

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