Let A,B,C be invertible matrices of size n×n. If tr(B-¹) =9 and A-¹=1/3, find ((AB)ᵀC)-¹ and compute tr(((AB)ᵀC)-¹ ).
a. ((AB)ᵀC)-¹ = 3B, tr(((AB)ᵀC)-¹ ) = 27
b. ((AB)ᵀC)-¹ = 3A, tr(((AB)ᵀC)-¹ ) = 27
c. ((AB)ᵀC)-¹ = 3C, tr(((AB)ᵀC)-¹ ) = 27
d. ((AB)ᵀC)-¹ = 3I, tr(((AB)ᵀC)-¹ ) = 27