WHAT IS DET(DET A) & also what isdet(adj A)?

Answer 1

Since det(A) is a scalar (a number), det(det(A))=det(A). Since A(adj A)=(det(A)*I, we get that det(A)*det(adj A)=(det(A))^n where A is an nxn matrix. Hence det(adj A)=(det(A))^(n-1).

Answer 2

What Is Det

Answer 3

Def DET:: if A= [a(ij)],
det A = |A| = a(i1)A(i1)+....+a(in)A(in) = a(1j)A(1j)+....+a(nj)A(nj)

det(det A) = || A || :)

adj A = [a(ji)] = B

check the def det B = det A

Answer 4

DET(DET A)=detA, since the determinant is just a number

since A^(-1)=AdjA/detA,
det(adjA)=det(detA*A(-1)) = detA^(-1) * detA = det(I)=n, where A is (n x n)

maybe?

Answer 5

Let A be a nxn matrix then
Det A=a (say)
Det(DetA)=Det(a)
=Det(a)xDet (I) [where I is an identity matrix &Det(I)=1]
=Det(aI)
=a^n
=(DetA)^n
Recall A^(-1)=(AdjA)/DetA
Multiply both sides by A
I=A*A^(-1)=(A*AdjA)/DetA
DetA*I=A*AdjA
Taking determinant of both sides
Det(DetA*I)=Det(A*AdjA)
Det(DetA)*Det I=DetA*Det(AdjA)
(DetA)^n=DetA*Det(AdjA)
(DetA)^n-1=Det(AdjA)