# Example 13 - Chapter 3 Class 12 Matrices

Last updated at Jan. 17, 2020 by Teachoo

Last updated at Jan. 17, 2020 by Teachoo

Transcript

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+1 × (−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

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

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.