Home
Class 12
MATHS
(A^(3))^(-1)=(A^(-1))^(3), where A is a ...

`(A^(3))^(-1)=(A^(-1))^(3)`, where A is a square matrix and `|A| ne 0`.

Text Solution

Verified by Experts

The correct Answer is:
True
Promotional Banner

Topper's Solved these Questions

  • SAMPLE QUESTION PAPER-II

    ACCURATE PUBLICATION|Exercise SECTION-B|8 Videos
  • SAMPLE QUESTION PAPER-II

    ACCURATE PUBLICATION|Exercise SECTION-C|8 Videos
  • SAMPLE QUESTION PAPER-I

    ACCURATE PUBLICATION|Exercise SECTION-D|6 Videos
  • SAMPLE QUESTION PAPER-II (SOLVED)

    ACCURATE PUBLICATION|Exercise SECTION-D|6 Videos

Similar Questions

Explore conceptually related problems

|A^(-1)| ne |A|^(-1) , where A is non-singular matrix.

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

(aA)^(-1)=(1)/(a)A^(-1) , where a is any real number and A is a square matrix.

If A is square matrix order 3, then |(A - A')^2015| is

Let A=[(1,0,0),(1,0,1),(0,1,0)] satisfies A^(n)=A^(n-2)+A^(2)-I for n ge 3 . And trace of a square matrix X is equal to the sum of elements in its proncipal diagonal. Further consider a matrix underset(3xx3)(uu) with its column as uu_(1), uu_(2), uu_(3) such that A^(50) uu_(1)=[(1),(25),(25)], A^(50) uu_(2)=[(0),(1),(0)], A^(50) uu_(3)=[(0),(0),(1)] Then answer the following question : Trace of A^(50) equals

State true/false:IF A is square matrix then | A^-1| = 1/|A|

True or False : If A is a square matrix and |A| ne 0, then (A^3)^-1 = (A^-1)^3)

If A^(n) = 0 , then evaluate (i) I+A+A^(2)+A^(3)+…+A^(n-1) (ii) I-A + A^(2) - A^(3) +... + (-1) A^(n-1) for odd 'n' where I is the identity matrix having the same order of A.

Find the sum of n terms of the series (a+b)+(a^(2)+ab+b^(2))+(a^(3)+a^(2)b+ab^(2)+b^(3))+"......." where a ne 1,bne 1 and a ne b .

For the matrix ( A=[[-3,6,0],[4,-5,8],[0,-7,-2]] ), find ( 1/2(A-A') ), where A' is the transpose of matrix A.