1. A matrix is said to be orthogonal if ATA = I. Thus the inverse of an orthogonal matrix is just its transpose. What are the possible values of det(A) if A is an orthogonal matrix?

In general, it is difficult to show that two matrices are similar. However, if two similar matrices are diagonalizable, the task becomes easier. In Exercises 38-41, show that A and B are similar by showing that they are similar to the same diagonal matrix. Then find an invertible matrix P such that .

If A and B are matrices and AB=0, msut |A|=0 or |B|=0? Explain.

11. Find two nonzero matrices and such that.