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 nand if A=B+C,BC=CB,C^(2)=O then without using mathematical induction, show that for any positive integer p,A^(p+1)=B^(p)[B+(p+1)C]

If B ,C are square matrices of order na n difA=B+C ,B C=C B ,C^2=O , then without using mathematical induction, show that for any positive integer p ,A^(p+1)=B^p[B+(p+1)C] .

If B ,C are square matrices of order na n difA=B+C ,B C=C B ,C^2=O , then without using mathematical induction, show that for any positive integer p ,A^(p-1)=B^p[B+(p+1)C] .

If B ,C are square matrices of order na n difA=B+C ,B C=C B ,C^2=O , then without using mathematical induction, show that for any positive integer p ,A^(p+1)=B^p[B+(p+1)C] .

If B ,C are square matrices of order na n difA=B+C ,B C=C B ,C^2=O , then without using mathematical induction, show that for any positive integer p ,A^(p+1)=B^p[B+(p+1)C] .

If B ,C are square matrices of order na n difA=B+C ,B C=C B ,C^2=O , then without using mathematical induction, show that for any positive integer p ,A^(p-1)=B^p[B+(p+1)C] .

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= .

Verify with square matrices of order 2: A(BC)=(AB)C

Verify with square matrices of order 2: A(B+C)=AB+AC