Let A,B,C,D,E be n*n matrices, each with non-zero determinant and ABCDE = I, where I = Identity matrix of order n, Then C =

Options :
  1. (B^-1)*(A^-1)*(E^-1)*(D*-1)
  2. (A^-1)*(B^-1)*(D^-1)*(E*-1)
  3. (ABDE)^-1
  4. (EDBA)*-1
Answer and Explanation :-

Answer: Option 1

Explanation:

ABCDE = I BCDE = (A^-1) Pre-Multiplying with A^-1 on both sides CDE = (B^-1)*(A^-1) Pre-Multiplying with B^-1 on both sides CD = (B^-1)*(A^-1)*(E^-1) Post-Multiplying with E^-1 on both sides C = (B^-1)*(A^-1)*(E^-1)*(D^-1) Post-Multiplying with D^-1 on both sides

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