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

# Let A be a 2×2 matrix with real entries, Let I be the 2×2 identity matrix. Denote by tr(A), the sum of diagonal entries of A. Assume that A2=I Statement 1: If A≠I and A≠−I, then detA=−1 Statement 2: If A≠I and A≠−I, then tr(A)≠0, then which of the following is correct

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

## The correct option is D Statement 1 is true, statement 2 is falseLet A=[abcd]. Then A2=[a2+bcab+bdac+dcbc+d2]=[1001] Hence det(A)=∣∣∣√1−bcbc−√1−bc∣∣∣=−1+bc−bc=−1 Here, we can see Tr(A)=0 so, 2nd statement is false only.

Suggest Corrections
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program