FP1 Matrix transformation

It's just a minor question but it keeps bugging me.

The question is from FP1 June 2009 (edexcel):

5. R = $\begin{pmatrix} a & 2 \\ a & b \end{pmatrix}$ , where a and b are constants and a > 0.
(a) Find R^2 in terms of a and b.

Given that R^2 represents an enlargement with centre (0, 0) and scale factor 15,
(b) find the value of a and the value of b.

So I solved it and got a = 3 (as per mark scheme) and b = 3 or b = -3. The mark scheme only provides b = -3 as the right answer.

Here is the answer to (a): $R^2 = \begin{pmatrix} a^2 + 2a & 2a + 2b \\ a^2 + ab & 2a + b^2 \end{pmatrix}$.

So obviously you equate the leading diagonal entries to 15 and solve for a and b. Since b is squared, I don't understand why it can't be either. Does it have to satisfy something in R? Is there anything else I've missed? Thanks in advance.

It's just a minor question but it keeps bugging me.

The question is from FP1 June 2009 (edexcel):

5. R = $\begin{pmatrix} a & 2 \\ a & b \end{pmatrix}$ , where a and b are constants and a > 0.
(a) Find R^2 in terms of a and b.

Given that R^2 represents an enlargement with centre (0, 0) and scale factor 15,
(b) find the value of a and the value of b.

So I solved it and got a = 3 (as per mark scheme) and b = 3 or b = -3. The mark scheme only provides b = -3 as the right answer.

Here is the answer to (a): $R^2 = \begin{pmatrix} a^2 + 2a & 2a + 2b \\ a^2 + ab & 2a + b^2 \end{pmatrix}$.

So obviously you equate the leading diagonal entries to 15 and solve for a and b. Since b is squared, I don't understand why it can't be either. Does it have to satisfy something in R? Is there anything else I've missed? Thanks in advance.

I'm quite rusty on this, but I think that if b = +3 then the off-diagonal elements are non-zero which means that your matrix isn't just a pure enlargement it is probably doing some sort of deformation like a shear to the target object as well!

Remember that a matrix that represents an enlargement with scale factor 15 will be:

$R^2 = \begin{pmatrix} 15 & 0 \\ 0 & 15 \end{pmatrix}$

Thus, your $2a + 2b$ $/$ $a^2 + ab$ should also equal zero, and that isn't satisfied by $b = 3$ if $a = 3$.

Oh obviously, that's so stupid of me. Thanks for help, gonna delete the thread in a couple of minutes.