Home
Class 12
MATHS
If A is a non - singular matrix then...

If A is a non - singular matrix then

A

`A^(-1)` is a non-singular matrix,

B

`A^(-1)`is skew-symmetric if A is symmetric

C

`abs(A^-1) = abs(A)`

D

`abs(A^-1) = abs(A)^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
A, D
`because abs(A) ne 0 rArr A^(-1) `
is also symmetric, if A is symmetric
and `abs(A^(-1)) = 1/abs(A) = abs(A) ^(-1)`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|16 Videos

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|10 Videos

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|30 Videos

  • MATHEMATICAL INDUCTION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|31 Videos

Similar Questions

Explore conceptually related problems

(Statement1 Assertion and Statement- 2 (Reason) Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice as given below. Statement - 1 If matrix A= [a_(ij)] _(3xx3) , B= [b_(ij)] _(3xx3), where a_(ij) + a_(ji) = 0 and b_(ij) - b_(ji) = 0 then A^(4) B^(5) is non-singular matrix. Statement-2 If A is non-singular matrix, then abs(A) ne 0 .

If P is non-singular matrix, then value of adj (P^(-1)) in terms of P is P//|P| b. P|P| c. P d. none of these

If A is a non-singular matrix of ordern, then |adj A| is equal to

If A is a non-singular matrix of order 3 and |A| = 2, then | adj A| equals

If A is a non-singular matrix of order 3 and |A| = 3, then |Adj. A| equals

If A is a non-singular matrix of order 3 and |A| = 4, then |Adj. A| equals

If A is a singular matrix, then adj A is a. singular b. non singular c. symmetric d. not defined

State whether it is true or false If A is a singular matrix then |A|=0 .