Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Let 
and let
and R = PQP -1
Then which of the following options is/are correct?
A
For x = 0, if 
, then a + b = 5
, then a + b = 5
B
For x= 1, there exists a unit vector 
for which 
for which
C
det R = det 
, for all 
, for all
D
There exists a real number x such that PQ = QP
Text Solution
Verified by ExpertsThe correct answer is:
C
(a, c)
R = PQP -1
det (R) = det (PQP -1 )
|R| = |PQP -1 |
= |P|.|Q|.|P -1 |
For x=0
Given, 
...(1)
...(2)
From (1) and (2)
2a = 4 
a = 2 and b = 3
So, a + b = 5.
For x = 1
det (R) = 48 - 4x 2 = 48 - 4 = 40
det (R) 
0
Hence, 
cannot a unit vector.
= 4(10-x 2 ) + 8
= 40-4x 2 + 8 = 48-4x 2 .
PQ = QP
If we equate a 12 from both
x + 4 + x = 2 + 2x
4 = 2
, no value exists.
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