Chapter 7.2, Problem 63E

Solution

To find: The determinant of square matrix $A$ and that is greater than equal to 0, justify your answer.

The given statement is false.

Given Information:

The determinant of square matrix $A$ is greater than equal to 0, justify your answer.

Explanation:

Consider the given statement,

The determinant can be any real number so it can also be negative. The given statement is false and taking an example to justify the matrix. For example, the  $2\times 2$  matrix defined as,

  $A=\left[\begin{array}{cc}1& 2\\ 2& 1\end{array}\right]$

Now, find the determinant.

  $\begin{array}{c}\left|A\right|=1\left(1\right)-2\left(2\right)\\ =1-4\\ =-3\end{array}$

Hence, the given statement is false.