If for the matrix `A ,\ A^3=I`
, then `A^(-1)=`
`A^2`
(b) `A^3`
(c) `A`
(d) none of these
Text Solution
Verified by Experts
We have given the matrix `A ,\ A^3=I`
`A^3=I`
`A^(−1)A A^2=A ^(−1)I`
`A^2=A ^(−1)`
Hence correct option is (b).
Topper's Solved these Questions
ADJOINTS AND INVERSE OF MATRIX
RD SHARMA|Exercise QUESTION|1 Videos
ALGEBRA OF MATRICES
RD SHARMA|Exercise Solved Examples And Exercises|410 Videos
Similar Questions
Explore conceptually related problems
Let A be a 3x3 matrix such that |A|=-2, then det(-2A^(-1))=-4 (b) 4(c)8(d) none of these
A square matrix A is said to be orthogonal if A^T A=I If A is a square matrix of order n and k is a scalar, then |kA|=K^n |A| Also |A^T|=|A| and for any two square matrix A d B of same order \AB|=|A||B| On the basis of above information answer the following question: IF A is a 3xx3 orthogonal matrix such that |A|=1, then |A-I|= (A) 1 (B) -1 (C) 0 (D) none of these
Let f(x)=(1+x)/(1-x). If A is matrix for which A^(3)=O,thenf(A) is (a)I+A+A^(2)(b)I+2A+2A^(2)(c)I-A-A^(2)(d) none of these
If A is an orthogonal matrix then A^(-1) equals A^(T) b.A c.A^(2) d.none of these
If A is a non singular matrix of order 3 then |adj(adjA)| equals (A) |A|^4 (B) |A|^6 (C) |A|^3 (D) none of these
If A is an invertible matrix then det(A^-1) is equal to (A) 1 (B) 1/|A| (C) |A| (D) none of these
((-3)/2)^(-1) is equal to 2/3 (b) 2/3 (c) 3/2 (d) none of these
If A is skew symmetric matrix of order 3 then det A is (A)0 (B)-A (C)A (D)none of these
If for a square matrix A,A^2=A then |A| is equal to (A) -3 or 3 (B) -2 or 2 (C) 0 or 1 (D) none of these
If A^(3)=O, then I+A+A^(2) equals I-A b.(I+A^(1))=^(-1) c.(I-A)^(-1) d.none of these