Define the n × n matrix In = (aij) by The matrix Iniscalledthe n × n identity matrix.Show...

Define the n × n matrix In = (aij) by

The matrix Iniscalledthe n × n identity matrix.

Show that if A is an  n × n matrix (Such a matrix is called  a square matrix), then

AIn = A = InA

An n × n matrix A is said to be invertible if there an n × n matrix B satisfying

AB = In = BA.