Transforming Tensor Components with Coordinate Systems

[peripatein]

Hi,

Homework Statement

The components of the tensor A^{i j} are A^{1 2} = A^{2 1} = A, whereas all the other components are zero. I am asked to write A(BAR)^{i j}, following a transformation to a new coordinate system, given that ∂q(BAR)^k/∂qⁿ = R_n^k. I am expected to write my answer in terms of R.

Homework Equations

The Attempt at a Solution

I know that A(BAR)^{i j} = ∂q(BAR)ⁱ/∂q^m * ∂q(BAR)^j/∂qⁿ * A^{m n}
But how may I proceed?

 

[peripatein]

I am wondering why no one has yet replied to this question.
Nevertheless, if anyone is reading this, I'd appreciate some help with this.
I happen to know that the answer is:
\bar{A}^ij = Rⁱ_lR^j_mA^lm, but how may I bring under account the fact that A^xy = A^yx = A?