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Example 21 - Verify (AB)’ = B’A’ if A = [-2 4 5] B = [1 3 -6] - Examples

  1. Chapter 3 Class 12 Matrices
  2. Serial order wise
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Example 21, If A =[■8(−2@4@5)], B = [1 3 -6], verify that (AB)’ = B’A’ Taking L.H.S Finding AB AB = [■8(−2@4@5)]_(3×1) 〖"[1 3 −6]" 〗_(1×3) = [■8(−2×1&−2×3&−2×(−6)@4×1&4×3&4×(−6)@5×1&5×3&5×(−6))]_(3×3) = [■8(−2&−6&12@4&12&−24@5&15&−30)] AB = [■8(−2&−6&12@4&12&−24@5&15&−30)] Now, (AB)’ = [■8(−2&4&5@6&12&15@12&−24&−30)] Taking R.H.S B’ A’ Finding B’ Given B = "[1 3 −6]" B’ = 〖"[1 3 −6]" 〗^′ = [■8(1@3@−6)] Now, A = [■8(−2@4@5)] A’ = [■8(−2@4@5)]^′= [ - 2 4 5] Finding B’A’ B’ A’ = [■8(1@3@−6)]_(3×1) 〖"[ − 2 4 5]" 〗_(1×3) = [■8(1×(−2)&1×4 &1×5@3×(−2)&3×4&3×5@−6×(−2)&−6×4&−6×5)]_(3×3) = [■8(−2&4&5@−6&12&15@12&−24&−30)] = L.H.S Hence L.H.S = R.H.S Hence proved

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