Construct two normal matrices A, B € M4, that are neither Hermitian or i times a Hermitian, by letting Re A = Re B be the matrix where every entry is 1 and finding nonzero Im A + Im B that commute with the Re A = Re B.

Show that no 22 matrices A and B exist that satisfy the matrix equation. AB-BA=1001.

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 .

Determine if the statement is true or false. If the statement is false, then correct it and make it true. For the product of two matrices to be defined, the number of rows of the first matrix must equal the number of columns of the second matrix.