Question

If a and b are different matrices satisfying a3 = b3 and a2b = b2a, then det (a2 + b2) is

Answer 1

Given: a and b are different matrices satisfying a³ = b³ and a²b = b²a

To find: det (a² + b²)

Solution:

• Now we have given :

                a³ = b³

• It can be written as: a³ - b³ = 0

                a²b = b²a

• It can be written as: a²b - b²a = 0

• Now we know that (a² + b²)(a - b) = a³ - a²b + ab² - b³

• So putting the values in it, we get:

                a³ - a²b + ab² - b³ = 0

• That means :

                (a² + b²) is a zero divisor.

                det(a² + b²) = 0

Answer:

              So the determinant is 0.