a) If A + B is also invertible, then show that A^-1 + B^-1 is also invertible by finding a formula for it. Hint: Consider A^-1(A+B)B^-1 and use Theorem 1.39.
Theorem 1.39 If A and B are invertible nxn matrices, then AB is invertible and (AB)^−1 = (B^-1)(A^-1)

b) Generalize the previous result: If cA + dB is invertible, for real numbers c and d then show that dA−1 + cB−1 is also invertible by finding a formula for it. Cite any theorems or definitions used.

Question

a) If A + B is also invertible, then show that A^-1 + B^-1 is also invertible by finding a formula for it. Hint: Consider A^-1(A+B)B^-1 and use Theorem 1.39. 
Theorem 1.39 If A and B are invertible nxn matrices, then AB is invertible and (AB)^−1 = (B^-1)(A^-1)

b) Generalize the previous result: If cA + dB is invertible, for real numbers c and d then show that dA−1 + cB−1 is also invertible by finding a formula for it. Cite any theorems or definitions used.