if B, C ARE n ROWED SQUARE MATRICES AND IF A=B+C , BC=CB ,C2=0 ,THEN SHOW THAT FOR EVERY n is the element ofN, A n+1 =Bn(B+(n+1)C).
Let P(n) be the statement given by
For n = 1, we have
Hence, the statement is true for n = 1.
Assume that the statement is true for n = k.
We shall now show that P(k + 1) is true. That is we need to show that
So, the statement is true for n = k + 1.
Thus, P(k) is true ÞP(k + 1) is true.
Hence, by the principle of mathematical induction P (n) is true for all n ÎN.