Your solutions are wrong since you didn't transpose.
The standard inner product for is the scalar product
You are only correct if the vectors are 1,1 but you can't make that assumption.
Dot product is not a matrix product of a row and column vector (so no transpose required). Plato's approach is correct and it is the approach that is expected (Your inner product is not a "dot" product as required by the question. You are assuming more knowledge on the part of the OP and so what you post is probably gobbledygook to them)