Answer:
Multiplication is commutative.
Step-by-step explanation:
Let n,m be two natural numbers.
We have to show that [tex]n\times m=m\times n[/tex]
We will prove this by induction
For n = 1, we have [tex]n\times 1 = 1\times n = n[/tex], which is true.
Let the given statement be true for n-1 natural numbers, that is,
[tex](n-1)\times m = m\times (n-1)[/tex]
Now, we have to show that it is true for n natural numbers.
[tex]nm = (n-1)m + m = m(n-1) + m[/tex]
which is equal to
[tex](m-1)(n-1) + (n-1) + m[/tex]
[tex]= (m-1)(n-1) + (m-1) + n[/tex]
[tex]= n(m-1) + n[/tex]
[tex]= (m-1)n + n[/tex]
[tex]= mn[/tex]
Hence, by principal of mathematical induction, the given statement is true for all natural numbers.
