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ifA is a matrix of order 3 such that A (ADJA ) = 10 I then determinant adj A

if a is the matrix of order 3 means its matrices of order 3*3,,

common form of matrices is =  (a11  a12  a13

                                                    a21 a22  a23

                                                    a31 a32 a33)

then cofactor matrices is     (c11  c12  c13

                                             c21  c22  c23

                                             c31  c32  c33) 

then as adjoint is the transpose of cofactor 

then adj =(c11  c21  c31

​                 c12  c22  c32

                 c13  c23  c33)  

then multiply a with adjoint matrices and equate it with 10..

hope it helps
 

  • 1
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we knows that det.adj a =det.,a to the power n-1

here the matrix is of 3*3 so,,value of n=3

det a=10

so,,10 tothe power 3-1

10 to the power2 =100

so determinant of adjoint a will be 100

hope it helps..thumbs up plzz

  • -2
  • We know that A* adj(A) =  |A|*I                                                                                                                                                                 -  --- therefore  |A|=10
  • |adj(A)| = An-1    (n= order of matrux)
  • therefore |adj(A)|= 103-1 = 102= 100
  • -1
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