5. Inverses and Determinants

Determinant Properties — Quiz

Test your understanding of determinant properties with 5 practice questions.

Practice Questions

Question 1

What is $\det(I_3)$, where $I_3$ is the $3 \times 3$ identity matrix?

Question 2

A matrix has two identical rows. What is its determinant?

Question 3

If $\det(A)=7$ and $B$ is obtained from $A$ by swapping two rows, what is $\det(B)$?

Question 4

Find the determinant of the matrix $\begin{pmatrix}2 & 0 & 1 \\ 0 & -3 & 5 \\ 0 & 0 & 4\end{pmatrix}$.

Question 5

If $\det(A)=5$ and $B=3A$, where $A$ is a $2 \times 2$ matrix, what is $\det(B)$?