I need help as I'm new to the topic and have difficulties solving this one.
Given $B^{-1} \times A^T$ = $\begin{bmatrix}0&1&2\\0&3&5\\-1&1&1\end{bmatrix}$
Find such $X$ that satisfies the equation: $A^T \times X \times B^{-1} = 2I$
I really tried in multiple ways and I can't make it through. Can you help?
I don't ask for the pure answer - I want to understand, any hints or tips would be appreciated.
Multiply the equation from the left by $(A^T)^{-1}$ and from the right by $B$. This yields $$X=2(A^T)^{-1}B=2(B^{-1}A^T)^{-1}.$$ Hence, we obtain $$X=\left(\begin{array}{ccc}-4&2&-2\\-10&4&0\\6&-2&0\end{array}\right).$$