Q:

Understanding the solution to a Matrix problem

I am trying to understand this matrix problem from my textbook. I was not able to understand 3 parts of the solution given there, which I have marked in yellow in the images below.
The question is:
Let A be matrix $\begin{bmatrix}2  & 3\\-1 & 2\end{bmatrix}$ and $f(x) = x^2 - 4A + 7I_2$. Show that $f(A) = O_{2*2}$. Use the result to find $A^5$.
Image 1
Image 2
Image 2 is a continuation of image 1.

The line above says $A^2 - 4A - 7I_2$ and in the next line they substitute $A^2$ with $(4A -7I_2)$. Whereas, as per my understanding the $A^2 = 4A + 7I_2$.
I don't understand how $(4A^2 - 7I_2A)$ became $4(4A - 7I_2) - 7A$
Same like 2 -> $36A^2 - 63I_2A - 112AI_2 + 196I_2I_2$ became $36(4A - 7I_2) - 63A - 112A + 196I_2$.

A:

The solutions manual is wrong. 
For q1: you're right; that substitution should have a plus sign rather than a minus sign
For q2: The solution book author has replaced $A^2$ with $4A - 7I$ again, so that $4\color{red}{A^2} - 7I_2A = 4\color{red}{(4A-7I)} - 7\color{green}{I_2A} = 4(A - 7I) - \color{green}{7A}$
For q3: The solution book author has made the same replacement of $A^2$ once more. 

