UPSC NDA I 2015 Mathematics Solved Paper

Consider the following matrices
A=(

x+y	y
2x	x−y

)
B=(

2

−1

)
AB=(

x+y	y
2x	x−y

)(

2

−1

)
=(

2x+2y−y

4x−x+y

)
=(

2x+y

3x+y

)
=C
=(

3

2

)
Therefore, by comparing the elements of the matrices, we get
2x+y=3;3x+y=2
Hence Solving for x and yields
x=−1,y=5
Therefore matrix A will be equal to
A=(

x+y	y
2x	x−y

)

=(

4	5
−2	−6

)
Hence,the required answer is
A2=(

4	5
−2	−6

)(

4	5
−2	−6

)
=(

6	−10
4	26

)