Combined and inverse transformations Quiz

1. Which matrix represents transformation $\mathbf{A}$ followed by transformation $\mathbf{B}$?

• A. $\mathbf{AB}$
• B. $\mathbf{BA}$
• C. $\mathbf{A}+\mathbf{B}$
• D. $\mathbf{A}^{-1}\mathbf{B}$

2. Find $\det\begin{pmatrix} 5 & 2 \\ 3 & 1 \end{pmatrix}$.

• A. $11$
• B. $1$
• C. $-1$
• D. $-11$

3. What is the inverse of a rotation through $40^\circ$ anticlockwise about $O$?

• A. Rotation through $40^\circ$ clockwise about $O$
• B. Rotation through $40^\circ$ anticlockwise about $O$
• C. Reflection in a line through $O$
• D. Enlargement with centre $O$ and scale factor $40$

4. A matrix has determinant $-5$. A triangle of area $4$ is transformed by it. What is the area of the image?

• A. $-20$
• B. $\frac45$
• C. $20$
• D. $1$

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

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