𝐴,𝐵,𝐶 are 𝑛×𝑛 invertible matrices. Simplify (𝐴𝐶)^−1𝐴𝐵(𝐶𝐵)^−1𝐶

Answer 1

(AC)^-1AB(CB)^-1C = C^-1A^-1ABB^-1C^-1C, But A^-1A = BB^-1 = C^-1C = I is identity matrix and because

(AC)^-1AB(CB)^-1C = C^-1