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Let A be 3x3 matrix such that AA=I and |A|=I, find the value of |A-I|

Let A be 3x3 matrix such that AA=I and |A|=I, find the value of |A-I|

Grade:12

4 Answers

Sunil Kumar
askIITians Faculty 183 Points
7 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
askIITians Faculty 33 Points
7 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
askIITians Faculty 33 Points
7 years ago
|A-I|^2=|A|^2-2|A|+1=0 since |A|=1
Thanks and Regards,
M.MURALIKRISHNA
askIITians faculty
Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
7 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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