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Let M be a 3 x 3 non-singular matrix with
$\det (M) = α . If M^{- 1} adj (adj M) = k I, then the value of k is$

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detailed solution

Correct option is B

We know that M (adj M) = det (M) I⇒ det⁡(M)M−1(adj⁡(adj⁡M))=α2I∵M−1=1|M|adj⁡(M)⇒ αM−1(adj⁡(adj⁡M))=α2I⇒ M−1(adj⁡(adj⁡M))=αI But, M−1(adj⁡(adj⁡M))=kHence, k=α

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Let M be a 3 x 3 non-singular matrix withdet⁡(M)=α. If M−1adj⁡(adj⁡M)=kI, then the value of k is

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free study material

Let M be a 3 x 3 non-singular matrix with
$\det (M) = α . If M^{- 1} adj (adj M) = k I, then the value of k is$