If a matrix $A$ has $12$ elements, what are the possible orders it can have?

Solution

1. A matrix with $n$ elements has an order $m\times n$ such that the product of the dimensions equals the total number of elements.
2. For a matrix with $12$ elements, we must identify all pairs of positive integers $(m,n)$ such that $m\times n=12$.
3. The factor pairs of $12$ are $(1,12),(2,6),(3,4),(4,3),(6,2),$ and $(12,1)$.
4. Hence the answer is (A).