Squaring Square Matrices

If you square a square matrix(or multiply it by itself) that has the exact same number in each of its cells, something interesting happens!


2 by 2 matrices

Here's what happens with 3 by 3 matrices:

3 by 3 matrices

Here's a 4 by 4 matrix:

I bet you can guess what will happen with a 5 by 5 matrix!

This trick will work as long as the matrix is square; in other words, the number of rows must be equal to the number of columns.

There's a function for this math trick. The function is:

y = zx2

x = the number in each matrix cell

y = the number of rows & columns multiplied by the square of the number in each matrix cell

z = the number of rows & columns

Y is the number you'll get in each cell of the equation matrix!

You can use any real number you want in this math trick, but remember that you must put the same number in each matrix cell!

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© Derek Cumberbatch