- #1

- 69

- 0

## Homework Statement

Assuming that all matrices are [itex]n\times n[/itex] and invertible, solve for [itex]D[/itex].

[itex]C^{T}B^{-1}A^{2}BAC^{-1}DA^{-2}B^{T}C^{-2}=C^{T}[/itex]

## The Attempt at a Solution

I tried to group all like terms and simplify. I'm pretty sure this is not allowed but I'm not really sure how to approach this question. Thanks a lot any help appreciated!

[itex]C^{T}C^{-1}C^{-1}C^{-1}B^{-1}BB^{T}AAAA^{-1}A^{-1}D=C^{T}[/itex]

[itex]C^{T}C^{-1}C^{-1}C^{-1}IB^{T}IIAD=C^{T}[/itex]

[itex]((C^T)^{-1}C^{T})C^{-1}C^{-1}C^{-1}B^{T}AD=C^{T}(C^T)^{-1}[/itex]

[itex]I(C^{-1}C^{-1}C^{-1}CCC)(B^{T}(B^T)^{-1})(AA^{-1})D=ICCC(B^T)^{-1}A^{-1}[/itex]

[itex]D=C^{3}(B^T)^{-1}A^{-1}[/itex]