Question

and BI
Now (AB) (B-'A-1) = A (BB-1) A-
by associative law.
= ALA-, from (2) = (AI) A-! by associative law.
= AA-), from (3) - I
from (1)
Again, (B-1A-_) (AB) = B-1 (A-'A) B
by associative law.
= BIB, from (1)
by associative law
B- B from (4)
I from (2)
Thus we get, (AB) (B-TA-!) = (B-1 A-1) (AB) = 1
Hence by definition of inverse of a matrix, we have (AB)-1 = B-1A!
-B- (IB).
Worked Out Example
1 2 3
Q. 1. Express 3 4 5 as the sum of a symmetric and a skew-
5 6 7
symmetric matrix.
1 2 3]
[135]​

Answer 1

Answer:

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