AP EAMCET Engineering 21 Apr 2019 Shift 2 Paper

(A)
The non-singular matrix of order 3,|A|=a
|(adjA−1)−1|=‌

1

|adjA−1|

=‌

1

|A−1|2

‌‌‌‌{|adjA|=|A|2,‌ if order of ‌A‌ is ‌3}
=‌

1

(‌ 1 |A| )2

=|A|2
=a2
(B)
It is given that for non-singular matrix A of order B,AB=0
(B) It is given that for non-singular matrix A of order B,AB=0
|AB|=0
|A||B|=0
|B|=0
And matrix B should be null matrix.
(C)
∆=|

1	x	x2
cos(a−b)‌y	cos‌a‌y	cos(a+b)‌y
sin(a−b)‌y	sin‌a‌y	sin(a+b)‌y

|
By simplify the above equation, we get
sin(by)−x‌sin(2by)+x2‌sin(by)
Thus, it doesn't depend on a
(D)
It is given that,
B=A−AT
BT=(A−AT)T
BT=AT−A
BT=−(A−AT)
BT=−B
B is a skew symmetric matrix.
Thus, |B|=0