What is 2 x 2 matrix multiplication?

One can use 2 x 2 matrix multiplication to multiply two 2 x 2 matrices together, resulting in another 2 x 2 matrix. Matrix multiplication is not commutative, which means that for matrices A and B, the product AB is not the same as BA.

One can consider multiplying a 2 x 2 matrix that has four elements, (a,b) in the top row and (c,d) in the bottom row, by another 2 x 2 matrix that has the elements (e,f) in the top row and (g,h) in the bottom row. By the rules of matrix multiplication, the resulting 2 x 2 matrix has the elements (ad + bf, ag + bh) in the top row and (ce + df, cg + dh) in the bottom row.