Last updated at Dec. 16, 2024 by Teachoo
To multiply two matrices,
We first write their order
For multiplication
Since 2 ≠ 3
We cannot multiply them
But, if we multiply BA
Then,
So, order of matrix after multiplication is
= 3 × 2
Let’s learn how to multiply them
So,
AB was not possible, but BA was possible
Thus, AB ≠ BA
Let’s do some more examples
So, multiplication is not possible
A = [■8(3&2@1&4)] & B = [■8(3&2@1&4@5&3)] A = [■8(3&2@1&4)]_(2 × 2) & B = [■8(3&2@1&4@5&3)]_(3 × 2) For multiplication 2 × 2 3 × 2 i.e B = [■8(3&2@1&4@5&3)]_(3 × 2) & A = [■8(3&2@1&4)]_(2 × 2) 3 × 2 2 × 2 3 × 2 2 × 2 They cancel out BA = [■8(3&2@1&4@5&3)]_(3 × 2) [■8(3&2@1&4)]_(2 × 2) 3 × 3 + 2 × 1 1 × 3 + 4 × 1 = [■8(9+2&6+8@3+4&2+16@15+3&10+12)]_(3 × 2) [■8(11&14@7&18@18&22)]_(3 × 2) = [■8(42&44@36&49@40&28)]_(3 × 2) Multiply [■8(3&2@1&4@5&3)] & [■8(9&5&2@1&8&5@3&1&6)] Our matrices are [■8(3&2@1&4@5&3)]_(3 × 2) [■8(9&5&2@1&8&5@3&1&6)]_(3 × 3) Since, They are not equal Multiply [■8(1@2@9@−8@−5@−4)] & [■8(0&−2&3&−15&6&−1)] [■8(1@2@9@−8@−5@−4)]_(6 × 1) [■8(0&−2&3&−15&6&−1)]_(1 × 6) = [■8(0&−2&3&−15&6&−1@0&−4&6&−30&12&−2@0&−18&27&−135&54&−9@0&16&−24&120&−48&8@0&10&−15&75&−30&5@0&8&−12&60&−24&4)] Multiply [■8(0&−2&3&−15&6&−1)] & [■8(1@2@9@−8@−5@−4)] [■8(0&−2&3&−15&6&−1)]_(1 × 6) [■8(1@2@9@−8@−5@−4)]_(6 × 1) = [0−4+27+120−30+4]_(1 × 1) =〖 [117]〗_(1 × 1)
Multiplication of matrices
About the Author
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo