 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2016/11/a/i/solution

(A B)^{T} = B^{T} A^{T} .

For the requested two-dimensional check, put

A = (a c b d)

and

B = (e g f h)

. Both sides are

(a e + b g a f + bh ce + d g c f + d h) .

More generally, the entry formula

(A B)_{ji} = \sum_{k} A_{jk} B_{ki}

is exactly

(B^{T} A^{T})_{ij}

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