Question

Let $A$ and $B$ be any two square matrices such that $AB=BA$, then by mathematical induction $(AB{)}^n=A^n{B}^n$ is true for

• A. all $n\in R$
• B. all $n\in N$
• C. all $n\in Z$
• D. all $n\in Q$

Answer 1

The correct option is B all $n\in N$

$\because$ AB and BA are equal

$\to$communicative property is true

${\left(AB\right)}^n=A^n{B}^n$

Matrice to the power fractions integers, complex number are not defined.

$\therefore R_1$ and z are eliminated

$\therefore$Answer is option B

all $nϵN$