# Multiplication of Two Matrices

In this page multiplication of two matrices we are going to see quiz on multiplying two matrices.

Multiplication of two matrices:

The product of matrix AB is determined by multiplying every row matrix of A multiplying by the column matrix of B.

Question 1:

Multiply the following matrices

A =

 1 3 7 4

B =

 -3 1 8 -7

Solution:

AB=

 1 3 7 4

x

 -3 1 8 -7

Here we have two rows and two columns each row must be multiplied with every column of the second matrix.

=

 1 3

x

 -3 8

 1 3

x

 1 -7

 7 4

x

 -3 8

 7 4

x

 1 -7

=

 (-3+24) (1-21) (-21+32) (7-28)

=

 21 -19 11 -21

Question 2:

Multiply the following matrices

A =

 5 11 3 -2

B =

 7 9 8 7

Solution:

AB=

 5 11 3 -2

x

 7 9 8 7

Here we have two rows and two columns each row must be multiplied with every column of the second matrix.

=

 5 11

x

 7 8

 5 11

x

 9 7

 3 -2

x

 7 8

 3 -2

x

 9 7

=

 (35+88) (45+77) (21-16) (27-14)

=

 123 122 5 13

Question 3:

Multiply the following matrices

A =

 -1 3 0 5

B =

 1 2 -3 7

Solution:

AB=

 -1 3 0 5

x

 1 2 -3 7

Here we have two rows and two columns each row must be multiplied with every column of the second matrix.

=

 -1 3

x

 1 -3

 -1 3

x

 2 7

 0 5

x

 1 -3

 0 5

x

 2 7

=

 (-1-9) (-2+21) (0-15) (0+35)

=

 -10 19 -15 35

Multiplication of Two Matrices to Matrix Introduction 