If A is non-singular matrix satifying AB-BA=A, then prove that det(B+I)=det(B-I)

If A is a nonsingular matrix satisfying AB-BA=A , then prove that det. (B+I)= det, (B-I) .

If is a non-singular matrix, then det (A^(1))=

If a and B are non-singular symmetric matrices such that AB=BA , then prove that A^(-1) B^(-1) is symmetric matrix.

If A is 3xx3 non-singular matrix such that A^(-1)+(adj.A)=0," then det "(A)=

If A is non-singular matrix and (A+I)(A-I) = 0 then A+A^(-1)= . . .

If B is a non-singular matrix and A is a square matrix,then det (B^(-1)AB) is equal to (A)det(A^(-1))(B)det(B^(-1))(C)det(A)(D)det(B)

If B is a non-singular matrix and A is a square matrix, then the value of det (B^(-1) AB) is equal to :

A is square matrix of order 2 such that A A^(T)= I and B is non-singular square matrix of order 2 and period 3 . If det (A)!=det(B), then value of sum_(r=0)^(20)det(adj(A^(r)B^(2r+1))) is (where A^(T) denotes the transpose of matrix A )

If x is a non singular matrix and y is a square matrix,such that det(x^(-1)yx)=K det y ,then find K