To find the number of matrices

Question

Is there any formula to find the number of all possible matrices of order n × n with each entry 0 or 1 ?

Pick whether $a_{1,1}$ is zero or one (two options). Pick whether $a_{1,2}$ is zero or one (two options)... repeat for each of the entries in the matrix. You had a total of $n^2$ such entries to decide their value with two options for each. Apply rule of product and conclude. — JMoravitz, Feb 23 '18 at 17:56
more interesting (and complicated) would have been if you were asking for the number of invertible square binary matrices. — G Cab, Feb 23 '18 at 18:19

score 2 · Accepted Answer · edited Feb 23 '18 at 18:06

2

We have 2 choices for $n^2$ entries thus for the Rule of product

$$\overbrace{2\cdot 2\cdot 2\cdot 2\cdot ...\cdot 2}^{\color{red}{n^2 \,times}}=2^{n^2}$$

edited Feb 23 '18 at 18:06

Adrian Keister

answered Feb 23 '18 at 17:58

user

score 2 · Answer 2 · answered Feb 23 '18 at 17:58

2

I'd say $2^{n^2}$ for you have 2 choices for each of the $n^2$ entries

answered Feb 23 '18 at 17:58

Nasenhaar

2 Answers2