[quad A^(n)=[[0,1,n],[0,0,1]]],[" 61.If "B," Care "n" rowed square matrices and if "A=B+C,BC=CB,C^(2)=0" ,then "s" batter "],[" every "n in N,A^(n+1)=B^(n)(B+(n+1)C)]

If B,C are n rowed square matrices and if A=B+C,BC=CB,C^(2)=O, then show that for every n in N,A^(n+1)=B^(n)(B+(n+1)C)

If B ,\ C are n rowed square matrices and if A=B+C , B C=C B , C^2=O , then show that for every n in N , A^(n+1)=B^n(B+(n+1)C) .

If B, C are a rowed squre matrices and if A=B+C, BC= CB, C^2=0, then show that A^(n-)=B^n(B+(n+1)C)AA^nin N.

If B,C are square matrices of order n and if A=B+C,BC=CB,C^(2)=0 then which of the following is true for any positive integer N

If B, C are square matrices of order n and if A = B + C , BC = CB , C^2=0 then which of the following is true for any positive integer N

if Aa n dB are squares matrices such that A^(2006)=Oa n dA B=A+B ,t h e n"det"(B) equals 0 b. 1 c. -1 d. none of these

if Aa n dB are squares matrices such that A^(2006)=Oa n dA B=A+B ,t h e n"det"(B) equals 0 b. 1 c. -1 d. none of these

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 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)^