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

1.	Adj(adj(......adj(A))) n times=?det(adj(adj(......adj(A))) n times=?please solve soon I will follow you
Answer» $\underline{\textsf{Given:}}$ $\textsf{A is a square matrix}$ $\underline{\textsf{To find:}}$ $\mathsf{det(adj(adj(........adj(A))))}\,\textsf{n times}$ $\underline{\textsf{Solution:}}$ $\underline{\textsf{Concept used:}}$ $\boxed{\begin{minipage}{6cm}$\textsf{If A be a square matrix order n,then}\\\\\mathsf{det(adj(A))=det(A)^{n-1}}$\end{minipage}}$ $\textsf{Let A be a square matrix of order m}$ $\textsf{Then,}$ $\mathsf{det(adj(adj(adj........adj(A))))}\;\;\textsf{n times}$ $\mathsf{=[det(adj(adj........adj(A)))]^{m-1}}\;\;\textsf{n-1 times}$ $\mathsf{=[[det(adj(........adj(A)))]^{m-1}]^{m-1}}\;\;\textsf{n-2 times}}}$ $\mathsf{=[det(adj(........adj(A)))]^(m-1)^2}}\;\;\textsf{n-2 times}$ $\textsf{Proceeding like this finally we get}$ $\mathsf{=[det(adj(A))]^(m-1)^{n-1}}\;\;\textsf{1 time}$ $\mathsf{=[det(A)^{m-1}]^(m-1)^{n-1}}\,$ $\mathsf{=[det(A)]^(m-1)^n}$ $\underline{\textsf{Answer:}}$ $\mathsf{det(adj(adj(........adj(A))))}\,\textsf{n times}\;\mathsf{=[det(A)]^(m-1)^n}$