The components of a matrix ${\mathbf{C}}=({C}_{i j})_{n\times n}$ are obtained from the components of two matrices ${\mathbf{A}}=({A}_{i j})_{n\times n}$ and ${\mathbf{B}}=({B}_{i j})_{n\times n}$ in the following way:
$${C}_{i j}=B_{i k} B_{j l} A_{k l} \tag{1}$$
Using Einstein's notation. I need to express $(1)$ as matrix multiplication.
My attempt
I know that for square matrices $n \times n$, if $\mathbf{c}=\mathbf{a}·\mathbf{b}$, then their components will satisfy that $$c_{i j}= a_{i k} b_{k j}$$
So, in $(1)$, $B_{i k} A_{k l}=X_{il}$ will correspond to the matrix multiplication $\mathbf{B}·\mathbf{A}=\mathbf{X}$, getting that
$${C}_{i j}= B_{j l} X_{il}$$
However, since the second index in $B_{j l}$ and the first index in $X_{il}$ doesn't match, how could this be expressed in terms of a matrix multiplication?
Dovetail indices. Since $C_{\color{red}{i}\color{limegreen}{j}}=B_{\color{red}{i}\color{blue}{k}}A_{\color{blue}{k}\color{brown}{l}}B^T_{\color{brown}{l}\color{limegreen}{j}}$, $C=BAB^T$.