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

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

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

If A = [(1,2,2),(2,1,-2),(a,2,b)] is a matrix satisfying A A^(T) = 9I_(3) , then the values of a and b are respectively A)1, 2 B) -1, 2 C) -1, -2 D) -2, -1

If A is an 3 xx 3 non - singular matrix such that AA'= A'A and B = A^(-1) A' , then BB' equals a)I + B b)I c) B^(-1) d) (B^(-1))

If A is a square matrix such that A^2=A , then (I+A)^3-7 A is equal to A) A B) I-A C) I D) 3A

If A is a singular matrix, then A adj A is: (i) Identity Matrix (ii) Scalar Matrix (iii) Null Matrix (iv) None of these

If A is an invertible matrix of order 2, then det( A^(-1) )=

If A is a square matrix such that A^2=A , then (I+A)^2-3A is equal to a)A b)I-A c)I d)3A

Let B is a square matrix of order 5, then abs[kB] is equal to….