Question

Find the inverse of A*B if
A⁻¹ = [-3 -1; 3 5]
B⁻¹ = [-5 0; -1 -2]

Answer 1

To find the inverse of A*B, multiply the inverses of A and B in the reverse order: (A*B)^-1 = B^-1 * A^-1.

Step-by-step explanation:

In order to find the inverse of A*B, we need to find the inverses of both A and B separately. The inverse of A is given as A-1 = [-3 -1; 3 5] and the inverse of B is given as B-1 = [-5 0; -1 -2]. To find the inverse of A*B, we simply multiply the inverses of A and B in the reverse order: (A*B)-1 = B-1 * A-1. Using the given values, we have (A*B)-1 = [-5 0; -1 -2] * [-3 -1; 3 5]. Multiplying these two matrices will give us the inverse of A*B.