Question

If A, C, D are matrices does (AC^-1)^-1(AC^-1)(AC^-1)^-1(AD^-1) simplify to to A^2(C)(D)

Answer 1

remembering that the inverse of the product of two matrices is the reverse product of the two inverses, then

(AC^-1)^-1 = CA^-1

(CA^-1)(AC^-1) = CC^-1 = I, the unit matrix, so we are left with

(AC^-1)^-1(AD^-1) = CA^-1AD^-1 = CD^-1

Answer 2

I thought (AC^-1)^-1 = AC?

Answer 3

Oh nvm that's where I went wrong, thank you!