wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Let A be a 2×2 matrix with non-zero entries and let A2=I, where I is 2×2 identity matrix. Define Tr(A) = sum of diagonal elements of A and |A|= determinant of matrix A.
Statement-1 Tr(A) =0 Statement-2: |A|=1

A
Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
Statement-1 is true, Statement-2 is false
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
Statement-1 is false, Statement-2 is true
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A Statement-1 is true, Statement-2 is false
Let A=(abcd), abcd 0
A2=(abcd)(abcd)
A2=(a2+bcab+bdac+cdbc+d2)
=a2+ bc =1, bc +d2=1
ab+bd=ac+cd=0
c0 and b0=a+d=0
Trace A=a+d=0a=d
|A|=ad bc =a2 bc =1
Hence, option 'B' is correct.

flag
Suggest Corrections
thumbs-up
1
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