Cubing Square Matrices

2 by 2 matrices

3 by 3 matrices

Do you see the pattern yet with the matrices on the bottom row above? The irrational number pi is in each cell of those matrices to give you a clue! If you still don't get it, the function can be found just below this paragraph!

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 = z²x³

x = the number in each matrix cell

y = the number of rows & columns squared multiplied by the cube 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!

Remember Math Trick #12: "Squaring Square Matrices"? Well the formula for that trick is multiplied by the product of the 2 variables z & x, which is zx! In other words, zx² * zx = z²x³

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!

Here's some additional information: Suppose you raised a square matrix to a power that's greater than 3? Well then y will be equal to z^3 * x^4 if you raise it to the power of 4; y will be equal to z^4 * x^5 if you raise it to the power of 5 & so on. You get the binomial pattern, don't you?

Note: Square matrices are the only matrices that can have exponents & the exponents can't be non-integers.