Linear algebra: determinants (proof)

[yoda05378]

hi, i seem to have some trouble proving:

Suppose M = [A B:O C], where A is a kxk matrix, C is a pxp matrix, and O is a zero matrix. Show that det(M) = det(A)det(C).


my attempt at a proof:

det(M) = det(A)det(C)

det[A B:O C] = det(A)det(C)

AC - OB = det(A)det(C)

AC = det(A)det(C) <-- doesn't make sense!

please point out where my logic failed.

 

[yoda05378]

nevermind. i figured out where i went wrong (i treated the matrices as if they were scalar, stupid me). thanks for all the help :sarcasm: