Problem
1. If AB = AC, where A is a square matrix, when does it necessarily follow that B = C? Give an example in which this does not follow.
2. A and B are symmetric matrices. Show that AB is also symmetric if and only if A and B are commutative.
3. If A is a square matrix, the matrix obtained by replacing each element of A by its cofactor and then transposing the resulting matrix is known as the ad joint of A and is denoted by Adj(A).
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.