Question

T/F 1. Let $A = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix}$, then $A^{-1} = \frac{1}{5} \begin{bmatrix} 2 & -3 \\ -1 & 4 \end{bmatrix}$. 2. For any $2 \times 2$ matrices A and B, AB = BA. 3. $\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \begin{bmatrix} 1 & 2 \\ 4 & 5 \end{bmatrix} = \begin{bmatrix} -3 & -3 \\ 8 & 10 \end{bmatrix}$. 4. Let $A = \begin{bmatrix} 1 & 0 \\ 0 & 2 \end{bmatrix}$, $B = \begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix}$ then A and B commute. 5. $\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} \begin{bmatrix} 1 & -1 & 1 \end{bmatrix} = 2$.

          T/F
1.
Let $A = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix}$, then $A^{-1} = \frac{1}{5} \begin{bmatrix} 2 & -3 \\ -1 & 4 \end{bmatrix}$.
2.
For any $2 \times 2$ matrices A and B, AB = BA.
3.
$\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \begin{bmatrix} 1 & 2 \\ 4 & 5 \end{bmatrix} = \begin{bmatrix} -3 & -3 \\ 8 & 10 \end{bmatrix}$.
4.
Let $A = \begin{bmatrix} 1 & 0 \\ 0 & 2 \end{bmatrix}$, $B = \begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix}$ then A and B commute.
5.
$\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} \begin{bmatrix} 1 & -1 & 1 \end{bmatrix} = 2$.

T/F
1.
Let A =
< b m a t r i x >, then A^-1 = (1)/(5)
< b m a t r i x >.
2.
For any 2 × 2 matrices A and B, AB = BA.
3.
< b m a t r i x >

< b m a t r i x >
=
< b m a t r i x >.
4.
Let A =
< b m a t r i x >, B =
< b m a t r i x > then A and B commute.
5.
< b m a t r i x >

< b m a t r i x >
= 2.

Added by Stephanie S.

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