Let A be 3x3 matrix such that AA=I and |A|=I, find the value of |A-I|
akash , 11 Years ago
Grade 12
4 Answers
Sunil Kumar
Last Activity: 11 Years ago
HI AKASH,
BY T I MEAN TRANSPOSE LIKE AT = TRANSPOSE OF A
det (A-I) = det(A-I) . detAT because (det A = det AT = 1)
= det(A.AT - AT) because (det AB = det A.detB)
= det(I - AT)= - det (AT -I)
= -det (A-I)T = -det(A-I) because I = I T AND (X+Y)T = XT + YT
= det (A-I) = 0
SUNIL KUMAR
IIT K
askiitians faculty
MuraliKrishna Medavaram
Last Activity: 11 Years ago
Let A be 3x3 matrix such thatAA=Iand |A|=1 then do like this A^2=I => A^2-I=0 (A-I)(A+I)=0 |A-I||A+I|=0 then |A-I|=0 thanks and regards M.MURALIKRISHNA askIITIANS FACULTY
MuraliKrishna Medavaram
Last Activity: 11 Years ago
|A-I|^2=|A|^2-2|A|+1=0 since |A|=1 Thanks and Regards, M.MURALIKRISHNA askIITians faculty
Sher Mohammad
Last Activity: 11 Years ago
See A^2=I => A^2-I=0 (A-I)(A+I)=0 |A-I||A+I|=0 |A-I|=0
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