Find the number of all possible matrices of order `3xx3` with each entry 0 or 1. How many of these are symmetric ?

Answer

`2^(9), 2^(6)`

Explanation

The given matrix of the order `3xx3` ha 9 elements and each of these elements can be either 0 or 1.
Now, each of the 9 elements can be chosen in two possible ways. Therefore, by the multiplication principle, the required number of possible matrices is `2^(9)=512`.
Each of the diagonal and upper triangle elements can be chosen in two ways.
So, number of symmetric matrices is `2^(6)`, as lower triangle elements are same as corresponding upper triangle elements.