Exercise 4.4.1

With the help of Theorem 4.8, the statement in row version or column version is equivalent. So we won’t mention it again and again.

1.

Yes. It’s Exercise 4.3.8.

2.

Ur...No! It’s wise to check whether there are any two identity rows or two identity columns first. How do we know what is wise?

3.

Yes. See the Corollary after Theorem 4.4.

4.

No. The determinant should be multiplied by $-1$.

5.

No. The scalar cannot be zero.

6.

Yes. Watch Theorem 4.6.

7.

Yes. This is Exercise 4.2.23.

8.

No. Read Theorem 4.8.

9.

Yes. Peruse Theorem 4.7.

10.

Yes. Glance the Corollary after Theorem 4.7.

11.

Yes. Gaze the Corollary after Theorem 4.7.