Home
Class 11
MATHS
If nth-order square matrix A is a orthog...

If nth-order square matrix A is a orthogonal, then `|"adj (adj A)"|` is

A

Statement -1 is True, Statement -2 is true, Statement -2 is a correct explanation for Statement-1.

B

Statement-1 is True, Statement -2 is True, Statement -2 is not a correct explanation for Statement -1.

C

Statement -1 is True, Statement -2 is False.

D

Statement -1 is False, Statement -2 is True.

Text Solution

Verified by Experts

The correct Answer is:
C
We have known that `abs (adj(adjA))=absA^((n-1)^2)`.
So, statement -2 is false.
If A is an orthogonal matrix, then`absA=pm1`
`:. Abs(adj(adjA))=absA^((n-1)^2)=(pm1)^((n-1)^2)=pm1`.
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    OBJECTIVE RD SHARMA|Exercise Exercise|80 Videos

  • MATRICES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos

  • MATRICES

    OBJECTIVE RD SHARMA|Exercise Section I - Solved Mcqs|57 Videos

  • LOGARITHMS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|21 Videos

  • MEAN VALUE THEOREMS

    OBJECTIVE RD SHARMA|Exercise Exercise|28 Videos

Similar Questions

Explore conceptually related problems

If nth-order square matrix A is a orthogonal, then |adj(adjA)| is (a)always -1 if n is even (b) always 1 if n is odd (c) always 1 (d) none of these

A square matrix B is said to be an orthogonal matrix of order n if BB^(T)=I_(n) if n^(th) order square matrix A is orthogonal, then |adj(adjA)| is

If A is order 3 square matrix such that |A|=2 , then |"adj (adj (adj A))"| is

If A is order 2 square matrix such that |A|=2, then |(adj(adj(adjA)))| is 512 b. 256 c. 64 d. none of these

If A is a square matrix of order n, then |adj (lambdaA)| is equal to

If A is a singular matrix, then A (adj A) is a

If A is a square matrix of order n xx n then adj(adj A) is equal to

" If "A" is a square matrix of order "n" ,then "|adj[lambda A)|" is equal to "