Statement 1: If the matrices $A,B,(A+B)$ are non – singular then ${\left[A{(A+B)}^{-1}B\right]}^{-1}=B^{-1}+A^{-1}$

Statement 2: ${\left[A{(A+B)}^{-1}B\right]}^{-1}={\left(A(A^{-1}+B^{-1})B\right)}^{-1}={\left((I+A{B}^{-1})B\right)}^{-1}={(B+AI)}^{-1}=B^{-1}+A^{-1}$

Both statement are true and statement 2 is correct explanation of statement 1

Both statement are true and statement 2 is incorrect explanation of statement 1

Statement 1 is true statement 2 is false

Statement 1 is false statement 2 is true