Q. 475.0( 2 Votes )

What is the total

Answer :

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.


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