$\newcommand{\ones}{\mathbf 1}$

The transpose of the matrix $\displaystyle \left[\begin{array}{cc} 1 & 2\\ 3 & 4\\ 5 & 6 \end{array}\right]$ is

$\displaystyle [1~2~3]^T+\left[\begin{array}{r} 4\\5\\6 \end{array}\right]$ is

If $\displaystyle Q = \left[\begin{array}{ccc} 1 & 2 & 0 \end{array}\right]$ and $\displaystyle R = \left[\begin{array}{r} -2 \\ -1 \\ 3 \end{array}\right]$, then the product $RQ$ is

If $A$ and $B$ are $3 \times 3$ matrices, then $AB \neq BA$.

• Incorrect.
• Correct! We usually do not have $AB=BA$, but there are cases when we do have $AB=BA$. One example: take $A=B=I$.

Let $\displaystyle A = \left[\begin{array}{ccc} 1 & 1 & 1\\ 0 & 1 & 1\\ 0 & 0 & 1 \end{array}\right]$. Then

Suppose $A$ and $B$ are $5 \times 5$ matrices. What is $(A+B)^2-(A-B)^2$?