 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2015/paper-1/18/b/solution

Interchanging the rows and columns gives the matrix transpose

A^{T} = 001100010 .

It cycles the three basis vectors in the opposite direction. Hence

A^{T} x = 001, (A^{T})^{2} x = 010, (A^{T})^{3} x = 100 .

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