Explain the term Comparable matrices?

Let B be a 4x4 matrix to which we apply the following operations:
1. double column 1,
2. halve row 3,
3. add row 3 to row 1,
4. interchange columns 1 and 4,
5. subtract row 2 from each of the other rows,
6. replace column 4 by column 3,
7. delete column 1 (column dimension is reduced by 1).
(a) Write the result as a product of eight matrices.
(b) Write it again as a product of ABC (same B) of three matrices.

Find a basis for the space of $2\times 2$ diagonal matrices.
$\text{Basis }=\{\left[\begin{array}{cc}& \\ & \end{array}\right],\left[\begin{array}{cc}& \\ & \end{array}\right]\}$

Tooth decay occurs when tooth enamel wears away over time. It exponential decay models the change in the number of dentists in the United States over time, do you think the number of dentists in the United States is increasing or decreasing?

Find the characteristic polynomial of the matrices
$\left[\begin{array}{ccc}1& 2& 1\\ 0& 1& 2\\ -1& 3& 2\end{array}\right]$

Write the given expression without the absolute value symbol. |x − y| − |y − x|

Let A and B be Hermitian matrices. Answer true or false for each of the statements that follow. In each case, explain or prove your answer. The eigenvalues of AB are all real.

write B as a linear combination of the other matrices, if possible.
$B=\left[\begin{array}{cc}2& 3\\ -4& 2\end{array}\right],A_1=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],A_2=\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right],A_3=\left[\begin{array}{cc}1& 1\\ 0& 1\end{array}\right]$