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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