Invertibility of Elementary Matrices Explain why all elementary matrices must be invertible. Demonstrate this property by finding the inverses of EInt, ERepl, or EScale in Problem.
Problem
Elementary Matrices If we perform a single row operation on an identity matrix, we obtain an elementary matrix EInt, ERepl, or EScale. Find the elementary matrices for each of the following row operations on I3.
(a) Interchange rows 1 and 2 (EInt).
(b) Add k times row 1 to row 3 (ERepl).
(c) Multiply k times row 2 (EScale).
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