Write the number of all possible matrices of order with each entry 1, 2 or 3.

Given: elements which can be used to form 2 × 2 order matrix are 1, 2 and 3

To find: Possible number of 2 × 2 order matrices which can be formed using given elements

Therefore,

Number of positions in a matrix are 4.

We have 3 elements to put in place of these 4 positions

So, for 1^st position i.e. X we have 3 options or elements

Similarly, for other 3 positions too we have 3 options

⇒ Possible number of 2 × 2 order matrices which can be formed using given elements = 3 × 3 × 3 × 3 = 81 matrices