Answer:
= 1(15?1)
+ 2 (?10?1) + 1(?2?3)
= 14 ? 22 ? 5 =
?13 0
Therefore A is
non-singular matrix so A?1
exists.
Here
A11 =
14; B12 = 11; B13 = ?5
A21 =
11; B22 = 4; B23 = ?3
A31 =
?5; B32 = ?3; B33 = ?1
Now
Let adj A = B
To find B?1
= 14 (?4 ?9) ?
11 (?11 ? 15) ? 5 (?33 + 20)
= ?182 + 286 +
65 = 169 0
Therefore B is
non-singular matrix so B?1 exists.
A11 =
?13; B12 = 26; B13 = ?13
A21 =
26; B22 = ?39; B23 = ?13
A31 =
?13; B32 = 13; B33 = ?65
adj
?.. (1)
Also Let A?1
= C
.. (2)
From (1) and
(2), we get
[adj A]?1
= adj (A?1)
Part (i)
is proved
Now
is also
non-singular matrix so C?1 exists
Hence part
(ii) is proved.
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