Question

What is the number of the possible square matrix of order $3$ with each entry $0$ or $1$? If your answer is $2^n$ , then find $n$.

Answer 1

A square matrix of order $3$ with each entry $0$ or $1$

Now for each entry we have $2$ choices, i.e., it can be filled in $2$ ways.

And there are $9$ places as it is a $3\times 3$ matrix.

Thus the total number of ways of filling all the entries are

$2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times =512$

$2^9=512$

$2^n=2^9$

$n=9$.