Determinants and inverse matrices Quiz

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

• A. $13$
• B. $15$
• C. $17$
• D. $-17$

2. A transformation has determinant $-3$. A triangle of area $4$ is mapped to a triangle of area

• A. $-12$
• B. $12$
• C. $\frac43$
• D. $7$

3. $\begin{pmatrix}2&k\\6&3\end{pmatrix}$ is singular. Then $k$ equals

• A. $1$
• B. $-1$
• C. $9$
• D. $4$

4. The inverse of $\begin{pmatrix}3&1\\5&2\end{pmatrix}$ is

• A. $\begin{pmatrix}2&-1\\-5&3\end{pmatrix}$
• B. $\begin{pmatrix}2&1\\5&3\end{pmatrix}$
• C. $\begin{pmatrix}-2&1\\5&-3\end{pmatrix}$
• D. $\begin{pmatrix}3&-1\\-5&2\end{pmatrix}$

5. If $\det\mathbf{A}=5$ and $\det\mathbf{B}=-2$, then $\det(\mathbf{AB})$ equals

• A. $3$
• B. $10$
• C. $-10$
• D. $-\frac52$