Question

adj(adj(......adj(A))) n times=?

det(adj(adj(......adj(A))) n times=?

please solve soon

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Answer 1

$\underline{\textsf{Given:}}$

$\textsf{A is a square matrix}$

$\underline{\textsf{To find:}}$

$\mathsf{det(adj(adj(........adj(A))))}\,\textsf{n times}$

$\underline{\textsf{Solution:}}$

$\underline{\textsf{Concept used:}}$

$\boxed{\begin{minipage}{6cm} \textsf{If A be a square matrix order n,then}\\\\\mathsf{det(adj(A))=det(A)^{n-1}} \end{minipage}}$

$\textsf{Let A be a square matrix of order m}$

$\textsf{Then,}$

$\mathsf{det(adj(adj(adj........adj(A))))}\;\;\textsf{n times}$

$\mathsf{=[det(adj(adj........adj(A)))]^{m-1}}\;\;\textsf{n-1 times}$

$\mathsf{=[[det(adj(........adj(A)))]^{m-1}]^{m-1}}\;\;\textsf{n-2 times}}}$

$\mathsf{=[det(adj(........adj(A)))]^(m-1)^2}}\;\;\textsf{n-2 times}$

$\textsf{Proceeding like this finally we get}$

$\mathsf{=[det(adj(A))]^(m-1)^{n-1}}\;\;\textsf{1 time}$

$\mathsf{=[det(A)^{m-1}]^(m-1)^{n-1}}\,$

$\mathsf{=[det(A)]^(m-1)^n}$

$\underline{\textsf{Answer:}}$

$\mathsf{det(adj(adj(........adj(A))))}\,\textsf{n times}\;\mathsf{=[det(A)]^(m-1)^n}$

Answer 2

Answer:

Step-by-step explanation: