The simplified form of ( ⁻¹ ( x y )- ⁻¹ ( x-y x+y ) ) is equal to

Step-by-step solution

Given that, ( ⁻¹ ( x y )- ⁻¹ ( x-y x+y ) ) [ array l = ⁻¹ ( x y )- ⁻¹ ( 1- y x 1+ y x ) = ⁻¹ ( x y )- ( ⁻¹ 1- ⁻¹ y x ) = ⁻¹ ( x y )+ ⁻¹ ( y x )- ⁻¹ 1 = ⁻¹ ( x y )+ ⁻¹ ( x y )- ⁻¹ 1 array ] Since, ( ⁻¹ x+ ⁻¹ x= I I 2 ) Then [ = I I 2 - ⁻¹ 1= I 2 - I 4 = I 4 ]