TS EAMCET 10-Sep-2020 Shift 1 Solved Paper

It is given that the matrices A and B are non-singular of order 3 and |B|=k,a positive integer, so
=‌

1

|B|3|A|

[∵|adj(A)|=|A|n−1, where n is the order of matrix A.]
Now, since it is given that BAB−1=I
⇒‌‌AB−1=B−1
=BAk−2(AB−1)=BAk−2B−1
∴‌‌BAkB−1=BAB−1=I
and,,B‌

adj(B)

|B|

=BB−1=I
Therefore, BAkB−1=B‌

adj(B)

|B|

, if BAB−1=I
Now, the adj (adj(A−1))=|A−1|3−2(A−1)
[∵ adj (adjA)=|A|n−2A where n is the order of matrixA]
=‌

1

|A|

(A−1)