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 falseLet A=(abcd), abcd ≠0A2=(abcd)⋅(abcd)A2=(a2+bcab+bdac+cdbc+d2)=a2+ bc =1, bc +d2=1ab+bd=ac+cd=0c≠0 and b≠0=a+d=0Trace A=a+d=0⇒a=−d|A|=ad− bc =−a2− bc =−1 Hence, option 'B' is correct.

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Adjoint and Inverse of a Matrix
MATHEMATICS
Watch in App
Join BYJU'S Learning Program