Let M=01a1233b1 and adj M=-11-18-62-53-1 where a and b are real numbers. Which of the following options is/are correct?
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a
a+b=3
b
detadjM2=81
c
adjM−1+adjM−1=−M
d
if Mαβγ=123 then α−β+γ=3
answer is A.
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Detailed Solution
AdjM=2−3b8b-6ab-1-3a33-2aa-1T=2−3bab-13-2a8-3aab-63-1Comparing b−6=−5⇒b=1 it gives 3−2a=−1⇒a=2a+b=3Option 1 is correct. 'M=8+21−6=−2β=−1,γ=1adj M2=M22=M4=16 Option 2 is correct adj M−1+adj M−1=2.MM=−M , option 3 is correct since adj A-1=Adet A Mαβγ=β+2γα+2β+3γ3α+β+γ=123 so α+β+γ=1⇒2α=2⇒α=1 it gives β=−1,γ=1so α−β+γ=3 option 4 is correct