Question

If a matrix $A$ consists of $n$ number of elements and $m$ is the possible number of order(s) for matrix $A$, where $(n>0),$ then which of the following is always correct

• A. $m=1,$ when $n$ is prime.
• B. $m=2,$ when $n$ is prime.
• C. $m>2,$ when $n$ is not prime.
• D. $m>2,$ when $n$ is prime.

Answer 1

The correct option is B $m=2,$ when $n$ is prime.

We know, for $n$ to be a prime number, have only two factors $1$ and $n.$
So, possible orders are $1\times n$ or $n\times 1.$ and
for non-prime number $(n\ne 1),$ have more than two factors.
So, for non-prime numbers $(n\ne 1)$, will have more than two possible orders.
But $1$ is not a prime number and for that only one possible order, i.e. $1\times 1.$