1.

Let A be a square matrix of order 2 such that A-1 =AA^(T) (where I is an identity matrix of order 2), then which one of the following is INCORRECT statement (where |A| represents determinant value of matrix A)

Answer»

|A|=1
adj A`=A^(-1)`
Trace of A=1
`A=A^(-1)`

Solution :`A -I =AA^(T)`…….(1)
TAKE TRANSPOSE both the SIDES
`A^(T) - I =AA^(T)`………..(2)
from (1) and (2) `A=A^(T)`
`rArr A-I =A^(2)`
`rArr |A| = 1, adj (A) = A^(-1)`
Trace of (A) =1


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