A matrix has 20 elements. The number of possible orders it can have is

The correct answer is Option (3) → 6

A matrix of order m × n has mn elements, so every way of writing 20 as a product of two natural numbers gives one order:

    \(20 = 1 \times 20\): orders \(1 \times 20\) and \(20 \times 1\)
    \(20 = 2 \times 10\): orders \(2 \times 10\) and \(10 \times 2\)
    \(20 = 4 \times 5\): orders \(4 \times 5\) and \(5 \times 4\)

Since 20 is not a perfect square, every pair gives two different orders. So there are 6 possible orders.