# What is the total number of 2 × 2 matrices with each entry 0 or 1?

Question:

What is the total number of $2 \times 2$ matrices with each entry 0 or $1 ?$

Solution:

In a $2 \times 2$ matrix, the total number of elements are 4 and each entry can be written in 2 ways.

Number of ways in which 4 entries can be written $=4^{2}=16$ [Applying the above property]