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VED1
E L-LOVELY-H math19-1 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 VIth 10-9-12

fJekJh^19 L gfotos ns/ ftgohs w?fNqe;

 2 3 B'N
=
−
;fjyzv 3 =+   = (10 9) 1
 3 5 
 1 3 
;fjyzv 5 =−   =− (5 6) =+
−
1
 2 5 
 1 2 
;fjyzv 12 =+   = (3 4) =−
−
1
 2 3 

T[bN t:{j d/ r[DXow (Properties of Inverse Matrices)

fe;h T[bNh w?fNqe; dk ftgohs (Inverse) ftbZyD j[zdk j?. ftbZyD dk noE j?^i/eo A dk
ftgohs B j?, sK B d/ fJbktk e'Jh d{ik w?fNqe; A dk ftgohs BjhA j?.
T[gZsh^i/eo ;zGt j?, sK wzB fbU B ns/ C d'B'A w?fNqe; A d/ ftgohs jB. T[d'A

A B = BA = I
ns/ AC = CA = I
AB = AC ⇒ B(AB) = B(AC)
⇒ (BA)B = (BA)C
⇒ IB = IC

⇒ B = C
(ii) i/eo A ns/ B T[bN w?fNqe; jB ns/ T[jBK dk eqw n j?, T[d'A T[jBK dk r[DB AB th T[bN j?
-1
-1
-1
ns/ (AB) = B A .
-1
-1
T[gZsh^feT[Ai' A ns/ B T[bN jB, fJ; bJh A ns/ B dk n;fsst j?l Bshi/ ti'L
-1
-1
-1
-1
(B A ) (AB) = B (A A) B ∴ r[DB ;fjukoh j?.
-1
-1
= B (IB) A A = 1
-1
= B B = I
-1
-1
-1
-1
d[pkok (AB) (B A ) = A (BB ) A
-1
= A (IA )
-1
= AA = I
-1
-1
-1
fJ; soQK AC T[bN j? ns/ (AB) = B A

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