What is the total number of 2 × 2 matrices with each entry 0 or 1?
We are given with the information that,
Each element of the 2 × 2 matrix can be filled in 2 ways, either 0 or 1.
We need to find the number of total 2 × 2 matrices with each entry 0 or 1.
Let A be 2 × 2 matrix such that,
Note that, there are 4 elements in the matrix.
So, if 1 element can be filled in 2 ways, either 0 or 1.
That is,
Number of ways in which 1 element can be filled = 21
Then,
Number of ways in which 4 elements can be filled = 24
⇒ Number of ways in which 4 elements can be filled = 16
Thus, total number of 2 × 2 matrices with each entry 0 or 1 is 16.