Question

The number of all possible square matrices of order $2$ formed by the elements $1,2$ and $3$ is ______

Answer 1

Let $A$ be the square matrix of order $2$ is given as :
$A=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$

Each element can be filled in three ways $1,2$ and $3$ and there are $4$ elements in this matrix.

So, the total number of matrices that can be formed is
$3\times 3\times 3\times 3=81$