×

# Matrix mania!

How do you find the number of possible matrices given that N number of elements(different elements) can be used to make a matrix of any order? For example: with 1 element you can make it only 1 matrix of order 1x1, with 2 elements (0,1) we can make 4 matrices of order 1x2, 2x1 and vice versa by interchanging the positions of the two elements respectively, etc. Do reply at thr earliest. I tried making a formula but it doesn't seem to work for 1 element.

Note by Toshali Mohapatra
9 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

\begin{align}\text{If }\hspace{2mm}N&=\prod(P_i)^{\alpha_{i}}\hspace{7mm}\color{blue}\text{where, }P_i \text{ denote the distinct prime factors of } N\\\\ \text{Then, } &\left(\prod(\alpha_{i}+1)\right)N!\hspace{4mm} \text{ will be your solution.}\\\\ \text{basically,}&\text{ it is equal to N! times the number of factors of the given number.}\end{align}

- 9 months ago

Gr8! Thanks a lot! How did u come up with such a solution?

- 9 months ago

The number of possible orders for the matrix is equal to the number of divisors of $$N$$ as for each divisor $$D$$,

$$N=D \times { \dfrac{N}{D}}$$

and for any matrix of a given order the elements can be swapped in N! ways

- 9 months ago