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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

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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)

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.