Find the values of a and b for which

Given :

To find : a and b

Formula used :

Where c_ij = a_i1b_1j + a_i2b_2j + a_i3b_3j + ……………… + a_inb_nj

If A is a matrix of order a b and B is a matrix of order c d ,then matrix AB exists and is of order a d ,if and only if b = c

=

= = =

=

Equating similar terms,

2a – b = 5

-2a – 2b = 4

Adding the above two equations,we get

-3b = 9

b = = -3

b = -3

substituting b = -3 in 2a – b = 5,we get

2a + 3 = 5

2a = 5 – 3 = 2

a = 1

a = 1 and b = -3