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Example 14 - Chapter 3 Class 12 Matrices
Last updated at Dec. 16, 2024 by Teachoo
Multiplication of matrices
Chapter 3 Class 12 Matrices
Concept wise
- Formation and order of matrix
- Types of matrices
- Equal matrices
- Addition/ subtraction of matrices
- Statement questions - Addition/Subtraction of matrices
-
Multiplication of matrices
- Statement questions - Multiplication of matrices
- Solving Equation
- Finding unknown - Element
- Finding unknown - Matrice
- Transpose of a matrix
- Symmetric and skew symmetric matrices
- Proof using property of transpose
- Inverse of matrix using elementary transformation
- Proof using mathematical induction
Transcript
Example 14 If A = [■8(1&0@0&−1)] and B = [■8(0&1@1&0)] , find AB and BA. Prove that AB ≠ BA AB = [■8(1&0@0&−1)] [■8(0&1@1&0)] = [■8(1(0)+0 (1)&1(1)+0 (0)@0(0)+(−1)(1)&0(1)+(−1) (0))] = [■8(0+0&1+0`@0−1&0+0)] = [■8(𝟎&𝟏@−𝟏&𝟎)] BA = [■8(0&1@1&0)][■8(1&0@0&−1)] = [■8(0(1)+1(0)&0(0)+1(−1)@1(1)+0 (0)&1(0)+0 (−1))] = [■8(0+0&0−1@0+1&0+0)] = [■8(𝟎&−𝟏@𝟏&𝟎)] ≠ AB Since AB ≠ BA Hence proved
