Question

Find the number of different $2\times 2$ matrices that can be formed with elements $1,2,3$ or $4$ with repetition.

Answer 1

The matrix $\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$; the values a, b, c and d can take any of the first four natural numbers. So, the variable 'a' has

$4$ possibilities b has $4$ possibilities, C has $4$ possibilities and d has $4$ possibilities. Hence the total number of possible matrices

$=4\times 4\times 4\times 4=256$ matrices.