For square matrix A show that |adj(adjA)|= |A|^(n-1)^2

Dear student,

if A is a non-singular square matrix of order n,then we know that
A(adjA)=AIn
A(adjA)=A0000A0000A0000An*n


A(adjA)=A0000A0000A0000A =An

as we know that AB=AB
AadjA=An
adjA=An-1
now if we replace A by adjA, we get
adj(adjA)=adjAn-1
adj(adjA)=(An-1)n-1
adj(adjA)=A(n-1)2

enjoy

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