# Maths-1996 -Set I

**Q1) Using elementary row transformations, find the inverse of the matrix
A = 4 5
3 4**

Ans1) Here

A =

4 5

3 4

and I =

1 0

0 1

Now A = IA

=>

4 5

3 4=1 0

0 1

A=> Applying R1 (1/4)R1

1 5/4

3 4=1/4 0

0 1

A=> Applying R2 R2 – 3R1

1 5/4

0 1/4

=

1/4 0

-3/4 1

A=> Applying R2 4R2

1 5/4

0 1=1/4 0

-3 4

A=> Applying R1 R1 – (5/4)R2

1 0

0 1

=

4 -5

-3 4

AA-1 = 4 -5

-3 4

Q2) For the matrices A and B, verify that (A, B)’ = A’B’ where

A = 1 2

3 4

B = 4 5

1 2

Ans2) Here

A = 1 2

3 4

B = 4 5

1 2= 6 9

16 23= 6 16

9 23

R.H.S. = B’A’ =4 1 1 3 = 6 16 = L.H.S.

5 2 2 4 9 23