Can someone help me?

Question

True or False
1. Only square matrices have multiplicative identities
2. Some square matrices do not have multiplicative inverses

Answer 1

1. Consider the orders of the matrices is a way to figure out this one. For a multiplicative identity, I, it means
I x M = M x I = M.

2. Such statement are more likely to be true. Consider matrices as transformations of points in a multi-dimensional space, inverses is to reverse the transformations. So, are there transformations that cannot be reversed? Consider a projection.