Using properties of determinants prove that:



Operating R1aR1, R2→bR2, R3cR3



Taking a, b, c common from C1, C2, C3 respectively



Operating R1R1- R3, R2R2- R3




Taking (a+b+c) common from R1, R2



Operating R3 R3- R1- R2




Operating C1aC1, C2bC2



Operating C1C1+C3, C2→C2+C3



Taking a, b, 2ab from R1, R2, R3



Expanding with R3





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