Question
Mathematics Question on Transpose of a Matrix
Let A=(02qrpq−rp−qr). If AAT=I3, then |p| is:
A
12
B
15
C
16
D
13
Answer
12
Explanation
Solution
Explanation:
Given:A=(02qrpq−rp−qr)We have to find the value of |p| if AAT=I3Consider:AAT=I3(02qrpq−rp−qr)(0pp2qq−qr−rr)=(100010001)(4q2+r22q2−r2−2q2+r22q2−r2p2+q2+r2p2−q2−r2−2q2+r2p2−q2−r2p2+q2+r2)=(100010001)After comparing, we getp2+q2+r2=1....(i)p2−q2−r2=0....(ii)Adding equation (i) and (ii)2p2=1p2=12p=12Hence, the correct option is (A).