Example 13 - Find AB, BA. Show that AB not = BA. A = [1 -2 3 - Examples

  1. Chapter 3 Class 12 Matrices
  2. Serial order wise
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Example 13 If A = [ 8(1& 2&3@ 4&2&5)] and B = [ 8(2&3@4&5@2&1)] then find AB, BA . Show that AB BA AB =[ 8(1& 2&3@ 4&2&5)]_(2 3 ) [ 8(2&3@4&5@2&1)]_(3 2) = [ 8(1 2+( 2) 4+3 2&1 3+( 2) 5+3 1@ 4 2+2 4+5 2& 4 3+2 5+5 1)]_(2 2 ) = [ 8(2 8+6&3 10+3@ 8+8+10& 12+10+5)] =[ 8(0& 4@10&3)] . BA = [ 8(2&3@4&5@2&1)]_(3 2) [ 8(1& 2&3@ 4&2&5)]_(2 3) = [ 8(2 1+3 ( 4)&2 ( 2)+3 2&2 3+3 5@4 1+5 ( 4)&4 ( 2)+5 2&4 3+5 5@2 1+2 ( 4)&2 ( 2)+1 2&2 3+1 5)]_(3 3 ) = [ 8(2 12& 4+6&6+15@4 20& 8+10&12+25@2 4& 4+2&6+5)] = [ 8( 10&2&21@ 16&2&37@ 2& 2&11)] AB Hence AB BA

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