Explain solution for rd sharma class 12 chapter Algebra of matrices exercise 4.3 question 61 math
Answer: Hence proved, for every integer .
Hint: We use the principle of mathematical induction.
Given: B, C are n rowed square matrix,
Squaring both sides, we get
[using distributive property]
[using BC=CB] given and put value of
Step 1: to prove P(1) is true, put n=1
From equation i, P(1)is true
Step 2: suppose P(k) is true
Step 3 : now we need to show that P(k+1) is true
That is we need to prove that
So, P(n) is true for n=k+1 whenever P(n) is true for n=k.
Therefore, by principle of mathematical induction P(n) is true for all natural number.