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(a)
(b)
Solve for .
18.
Show that the value of the determinant
19.
does not depend on , using the method of this section.
Prove that the matrices
20.
commute if and only if
Explain why the determinant of an matrix with integer entries must be an integer, using the
21. method of this section.
What can you say about the determinant of an matrix all of whose entries are 1? Explain your
22. reasoning, using the method of this section.
23.
(a) Explain why the determinant of an matrix with a row of zeros must have a zero
determinant, using the method of this section.
(b) Explain why the determinant of an matrix with a column of zeros must have a zero
determinant.
