 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2022/digital-systems-linear-algebra-introduction-to-formal-proof-resit/5/c/solution

Multiply the original equation on the left by

A^{- 1}

to obtain

B = A + I + A^{- 1} .

Each term on the right commutes with

A

. Thus

B A = A^{2} + A + I = A B .

No general commutativity of matrix multiplication is being assumed; it follows from this particular expression for

B

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