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Let A,B and C be square matrices of orde...

Let `A,B` and `C` be square matrices of order `3xx3` with real elements. If `A` is invertible and `(A-B)C=BA^(-1),` then

A

`C(A-B)=BA^(-1)`

B

`C(A-B)=A^(-1)B`

C

`(A-B)C=A^(-1)B`

D

`C(B-A)=A^(-1)B`

Text Solution

Verified by Experts

The correct Answer is:
B
`(A-B)C+BA^(-1)`
`impliesAC-BC-BA^(-1)+"AA"^(-1)=I_(3)`
`implies(A-B)(C+A^(-1))=I_(3)implies(A-B)^(-1)=C+A^(-1)`
`implies(C+A^(-1))(A-B)=I_(3)`
`impliesC(A-B)+A^(-1)A-A^(-1)B=I_(3)`
`impliesC(A-B)=A^(-1)B`
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