If A and B are square matrices of the same order and A is nonsingular, then for a positive integer n, `(A^(-1)BA)^(n)` is equal to

If Aa n dB are square matrices of the same order and A is non-singular, then for a positive integer n ,(A^(-1)B A)^n is equal to A^(-n)B^n A^n b. A^n B^n A^(-n) c. A^(-1)B^n A^ d. n(A^(-1)B^A)^

If A and B are square matrix of same order then (A-B)^(T) is:

If A and B are symmetric matrices of same order than AB-BA is a:

If A and B are two invertible matrices of the same order, then adj (AB) is equal to

If A and B are two nonzero square matrices of the same order such that the product AB=O , then

If A and B are square matrices of same order such that AB=O and B ne O , then prove that |A|=0 .

If A, B, and C are three square matrices of the same order, then AB=AC implies B=C . Then

If A and B are square matrices of the same order such that AB = BA, then prove by induction that AB^(n)=B^(n)A . Further, prove that (AB)^(n)=A^(n)B^(n) for all n in N .

If B ,C are square matrices of order na n difA=B+C ,B C=C B ,C^2=O , then for any positive integer p ,A^(p-1)=B^p[B+(p+1)C] where k= .

If Aa n dB are two non-singular matrices of the same order such that B^r=I , for some positive integer r >1,t h e nA^(-1)B^(r-1)A=A^(-1)B^(-1)A= I b. 2I c. O d. -I