Matrix Magic 3

This math trick proves that matrix multiplication is at least sometimes commutative!

Examples:

If every cell of a square matrix is exactly the same number & multiplied by another square matrix that has cells that are all equal to each other, then even if you swap them, the product matrix will be exactly the same! The order of the matrices WON'T matter! The number that you get in each cell of the product matrix depends on the number of rows & columns of Matrices A & B. The formula is just below:

w = xyz

w = the number in each cell of the product matrix

x = the number in each cell of Matrix A

y = the number in each cell of Matrix B

z = the number of rows & columns in Matrices A & B

The product of the numbers in the cells of Matrices A & B gets multiplied by the number of rows & columns. In the 1st example, 20 (the product of 4 & 5) is multiplied by 2, giving 40. In the 2nd example, 18 (the product of 3 & 6) is multiplied by 3, giving 54.

If both square matrices shared the exact same number in each of their cells, then that would make them exactly the same! In other words, you would be squaring a single square matrix!

Back to Index Page Back to Math Trick Menu