Question

Let a and b be n × n matrices. Show that (a - b)² = a² - ab - ba + b²?

Answer 1

To show that (a - b)² = a² - ab - ba + b², we can expand the equation using the distributive property and FOIL method.

Step-by-step explanation:

To show that (a - b)² = a² - ab - ba + b², we can expand the equation using the distributive property. First, we square (a - b) by multiplying it by itself:

(a - b)² = (a - b)(a - b)

Next, we use the FOIL method to multiply the terms:

(a - b)(a - b) = a(a - b) - b(a - b) = a² - ab - ba + b²

Thus, we have shown that (a - b)² = a² - ab - ba + b².