Class 12 Maths Matrices | Multiplication of 2 matrices |

**Multiplication of 2 matrices**

Let take scenario where

Amit wants to buy 5 eraser 7 pencils & Aditi wants to buy 3 eraser 4 pencils

Price at shop 1: Eraser 6, Pencil 7 & Price at shop 2 : eraser 4, Pencil 6

What will be the cost when Amit & Aditi buys these items from Shop 1 & Shop 2.

We can represent this data using matrix & use the concept of multiplication of two matrices to find the total price.

Using the Product of Matrices we can say that Amit will have to pay 79 if he buys from shop 1 & 62 if he has to buy from shop 2. Similarly Aditi has to pay 46 if she buys from shop 1 & 35 if she buys from shop 2.

The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. Let A = [a_{ij}] be an m × n matrix and B = [b_{jk}] be an n × p matrix. Then the product of the matrices A and B is the matrix C of order m × p. To get the (i, k)^{th} element c_{ik} of the matrix C, we take the i^{th} row of A and k^{th} column of B, multiply them element wise and take the sum of all these products

Note: If AB is defined, then BA need not be defined

For approach to multiplication refer ExamFear video lessons.

**Numerical**:

**Solution**:

**Zero matrix as the product of two non zero matrices**

We know that, for real numbers a, b if ab = 0, then either a = 0 or b = 0. This need not be true for matrices.

Eg

Here A x B = 0

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**Properties of multiplication of matrices**

- The associative law
- The distributive law
- The existence of multiplicative identity

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