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,
A = \( \begin{bmatrix}
a_{11} & a_{12} \\[0.3em]
a_{21} & a_{22}\\[0.3em]
\end{bmatrix}\)
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.
