Answer:
See explanation below
Step-by-step explanation:
By definition of inverse we know that an operation multiplied by its inverse gives us 1.
Therefore we can multiply (AB)⁻¹ by AB and the result will be 1
(AB)(AB)⁻¹ = 1
A⁻¹(AB)(AB)⁻¹= A⁻¹ (we multiplied both sides by A⁻¹ and on the left side now we have (A)(A)⁻¹= 1)
1·B(AB)⁻¹ = A⁻¹
B(AB)⁻¹ = A⁻¹
B⁻¹B(AB)⁻¹ = B⁻¹A⁻¹ (we multiplied both sides by B⁻¹ and on the left side we have B⁻¹B = 1)
1·(AB)⁻¹ = B⁻¹A⁻¹
Therefore, (AB)⁻¹ = B⁻¹A⁻¹
