Shilov Chapter 4 Problem 16 I am working on the captioned problem which is reproduced below.

And the hint for this problem is the following:

But I have no idea of how to use Chapter 3 Prob 12 for this problem. That problem is reproduced here:

I have no problem in finding out that three equations for unknown elements of A and B lead to equations for three minors of 2x3 matrix. But I have no clue as to how to proceed using Chap3 Prob 12.
Thank you.

The equation
$$
\pmatrix{a&b\\ c&d}\pmatrix{x&y\\ z&w}=\pmatrix{P&-Q\\ R&-P}
$$
can be rewritten as
\begin{aligned}
bz-cy &= P,\\
(a-d)y-b(x-w) &= -Q,\\
c(x-w)-(a-d)z &= R.
\end{aligned}
That is, if
$$
A=\pmatrix{b&c&a-d\\ y&z&x-w},\tag{$\ast$}
$$
then the minors obtained by deleting respectively the third column, the second column and the first column of $A$ are given by $P,Q$ and $R$. So, if one can construct $A$, one can pick two arbitrary values for $d$ and $w$ and recover $a,b,c,x,y,z$ from $(\ast)$.
