Home
Class 12
MATHS
Let A be a square matrix of order 2 such...

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)

A

|A|=1

B

adj A`=A^(-1)`

C

Trace of A=1

D

`A=A^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
D
`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
Promotional Banner

Similar Questions

Explore conceptually related problems

If A is square matrix of order n gt 1, then which one of the following is correct ?

If A is a square matrix of order n gt 1 , then which one of the following is correct ?

" Which one is the identity matrix of order "2" "

|adjA|=|A|^(2) where A is a square matrix of order two.

Let A be a matrix of order 3 such that A^(2)=3A-2I where, I is an identify matrix of order 3. If A^(5)=alphaa+betaI , then alphabeta is equal to

If A is a square matrix of order n and AA^(T)=I then find |A|

Let A be a 3xx3 square matrix such that A(a d j\ A)=2I , where I is the identity matrix. Write the value of |a d j\ A| .

A square matrix A of order 3 satisfies A^(2)=I-2A , where I is an identify matrix of order 3. If A^(n)=29A-12I , then the value of n is equal to

A square matrix M of order 3 satisfies M^(2)=I-M , where I is an identity matrix of order 3. If M^(n)=5I-8M , then n is equal to _______.