Question

prove that adj A=An-1 where n is order of matrix

Answer 1

It is known that,

A^(-1)=adj(A)/det(A)…..’(A^(-1))’ denotes inverse of the matrix A.

Therefore we can write,

A×adj(A)=(det(A))^n

In other words:

Adj(A)=(det(A)^n)/A…..

Taking determinant on both sides,

Det(adj(A))=(det(A)^n)/det(A)

Thus,

Det(adj(A))=det(A)^(n-1)

Good luck…