Chapter 5.5, Problem 4E

In ${ℝ}^{n\times m}$ , consider the inner product $\langle A,B\rangle =trace\left(A^{T}B\right)$ defined in Example 3.
a. Find a formula for this inner product in ${ℝ}^{n\times 1}={ℝ}^n$ .
b. Find a formula for this inner product in ${ℝ}^{1\times m}$ (i.e.,the space of row vectors with m components).