CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If A be a non-singular matrix of order 2, such that A+|A|adj(A)=0, then which of the following option(s) is/are always correct ?
(where adj(A) is the adjoint of matrix A )

A
|A|=1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
the trace of matrix A is 0.
(the trace of a square matrix is the sum of elements on the main diagonal)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
A|A|adj(A)=2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
A|A|adj(A)=4
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct options are
A |A|=1
B the trace of matrix A is 0.
(the trace of a square matrix is the sum of elements on the main diagonal)
D A|A|adj(A)=4
Let A=[a1a2a3a4]
|A|=a1a4a2a3=k(say)

adj(A)=[a4a2a3a1]

A+|A|adj(A)=0
[a1+ka4a2ka2a3ka3a4+ka1]=0
k[1+a24+a21+k2+2a2a3]=0
(a4+a1)2+1+k22(a1a4a2a3)=0(a4+a1)2+1+k22k=0
k=|A|=1 & a4+a1=0

A|A|adj(A)=Aadj(A) (|A|=1)
=[a1a42a22a3a4a1]
=2a1a4a21a244a2a3
=4a1a4(2a1a4+a21+a24)4a2a3
=4(a1a4a2a3)(a1+a4)2
=40
=4

flag
Suggest Corrections
thumbs-up
7
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Adjoint and Inverse of a Matrix
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon