You try to calm them down, saying "Don’t worry, the matrix also satisfies PA = I, and therefore P is the inverse of A just like you wanted. I’ll prove it to you..." Your proof consists of the following two steps (fill in the details as your answer to this question): Step 1: Argue that your matrix P is the unique Q ∈ R n×n satisfying AQ = I. Step 2: Prove that PA = AP = I. (Hint: consider the matrix A(P+PA−I))