OCR A-Level Further Maths A matrices and transformations overview quiz quiz

$\mathbf{A}\mathbf{B} = \mathbf{B}\mathbf{A}$

$\mathbf{A}\mathbf{B} \ne \mathbf{B}\mathbf{A}$

$\mathbf{A}\mathbf{B} = \mathbf{0}$

$\mathbf{A} + \mathbf{B} = \mathbf{A}\mathbf{B}$

$ad + bc$

$ab - cd$

$ad - bc$

$ac - bd$

it is symmetric

all entries are positive

it is a $3 \times 3$ matrix

its determinant is non-zero

$\frac{1}{ad - bc}\begin{pmatrix} d & -b \\ -c & a \end{pmatrix}$

$\frac{1}{ad - bc}\begin{pmatrix} a & -b \\ -c & d \end{pmatrix}$

$\begin{pmatrix} d & -b \\ -c & a \end{pmatrix}$

$\frac{1}{ad + bc}\begin{pmatrix} d & b \\ c & a \end{pmatrix}$

angle of rotation

area scale factor

number of invariant points

length of the longer column

$\mathbf{P}\mathbf{Q}$

$\mathbf{P} + \mathbf{Q}$

$\mathbf{Q}\mathbf{P}$

$\mathbf{P}\mathbf{Q}^{-1}$

$\begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}$

$\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}$

$\begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix}$

$\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$

$\mathbf{B}^{-1}\mathbf{A}^{-1}$

$\mathbf{A}^{-1}\mathbf{B}^{-1}$

$\mathbf{A}^{-1} + \mathbf{B}^{-1}$

$(\mathbf{B}\mathbf{A})^{-1}$

the matrix of cofactors without transposing

the transpose of the matrix of cofactors

the matrix divided by its determinant

the transpose of the matrix of minors

meet at a single unique point of intersection

are all parallel with no points in common

form a sheaf meeting in a common line

are mutually perpendicular to one another

$\mathbf{M}\mathbf{x} = \mathbf{0}$

$\det \mathbf{M} = 1$

$\mathbf{M}\mathbf{x} = -\mathbf{x}$

$\mathbf{M}\mathbf{x} = \mathbf{x}$

$\frac{1}{4}$

$\frac{1}{12}$

$-\frac{1}{4}$

$\frac{1}{16}$