SOLUTION: Please help Suppose A, B and AB-I are non-degenerate and have same order. Prove that (1) {{{A - B^-1}}} is non-degenerate. (2) {{{(A - B^-1)^-1

SOLUTION: Please help Suppose A, B and AB-I are non-degenerate and have same order. Prove that (1) {{{A - B^-1}}} is non-degenerate. (2) {{{(A - B^-1)^-1 - A^-1}}} is non-degenerate.

Question 1099395: Please help
Suppose A, B and AB-I are non-degenerate and have same order. Prove that
(1) is non-degenerate.
(2) is non-degenerate. find the inverse of this matrix.
Answer by ikleyn(52784) (Show Source): You can put this solution on YOUR website!
.

1)  Since the matrix B is non-degenerated, it has the inverse matrix  .


    Multiply the matrix  by the matrix   on the right. You will get

     = .


    Since both matrices on the left side of the equation are non-degenerated, their product on the right side is non-degenerated, too.


    QED

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