Consider the matrix\

A=[[1,2,3],[-4,5,6],[-7,8,9]]

\ Let

C_(i,j)

denote the cofactor of the ith row and

j

th column of

A

.\ (a) The matrix of cofactors of

A

is

cof(A)=[[-3,-6,(C_(1,3))],[(C_(2,1)),30,-22],[-3,(C_(3,2)),13]]

. Find

adj(A)

,\ the adjoint of

A

.\ (b) Find

A^(-1)

.

8. Consider the matrix A=147258369 Let Ci,j denote the cofactor of the i th row and j th column of A. (a) [6 pts.] The matrix of cofactors of A is cof(A)=3C2,13630C3,2C1,32213. Find adj(A), the adjoint of A. (b) [4 pts. ] Find A1