Find, if possible, a matrix Y such that (Y + BCT)-1 = A

Question

Here is the question

Question

and I am asked to "find, if possible, a matrix Y such that (Y + BCT)-1 = A"

my answer was:

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is it right? what makes me uncertain of my answer is moving matrix Q for example to the other side of the equal sign makes it (Q inverse) ? in all cases(addition and multiplication?

Answer 1

I got the same question. I guess it is y = A - (BC-1)T