[Math] Finding the matrix of the linear transformation T(x) = B(A(x))

linear algebralinear-transformationsmatricesvectors

"Let A = \begin{pmatrix}3&1\\ 9&6\end{pmatrix}

and B = \begin{pmatrix}5&8\\ 4&2\end{pmatrix}

What is the matrix C of the linear transformation T(x) = B(A(x))?"

I am confused by this question because it does not refer to the typical reflection across a line. Instead, it seems like I have to reflect it by merging the two matrices together. Would this involve a similar approach or something slightly more different?

Any help?

Best Answer

Here, the linear transformation is from $\Bbb R^2$ to $\Bbb R^2$ and will be $T(x) = (BA)x$

So when we will consider the standard basis both sides,then the matrix of representation will be $BA$.

Hence $C= BA$ will be the answer.

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