The n × n identity matrix, denoted I or In, is the matrix whose iith entry is 1 and whose other entries are
all zero. That is,
(a) Explicitly write out I2, I3, and I4.
(b) The reason I is called the identity matrix is that it behaves as follows: Let A be any m × n matrix. Then
i. AIn = A.
ii. Im A = A.
Prove these results. (Hint: What are the ijth entries of the products in (i) and (ii)?)
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