If `A` is an orthogonal matrix then `A^(-1)` equals `A^T` b. `A` c. `A^2` d. none of these

If for the matrix A ,\ A^3=I , then A^(-1)= A^2 (b) A^3 (c) A (d) none of these

A square matrix A is said to be orthogonal if A^T A=I If A is a sqaure 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 abov einformation answer the following question: If A is an orthogonal matrix then (A) A^T is an orthogonal matrix but A^-1 is not an orthogonal matrix (B) A^T is not an orthogonal mastrix but A^-1 is an orthogonal matrix (C) Neither A^T nor A^-1 is an orthogonal matrix (D) Both A^T and A^-1 are orthogonal matices.

If A is an invertible matrix then det(A^-1) is equal to (A) 1 (B) 1/|A| (C) |A| (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

If A is a 3xx3 skew-symmetric matrix,then trace of A is equal to -1 b.1 c.|A| d.none of these

(-A)^(-1) is always equal to (where A is nth- order square matrix) (-A)^(-1) b.-A^(-1) c.(-1)^(n)A^(-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

Let A = [{:(0, 2b , c),(a, b, -c),(a, -b, c):}] be an orthogonal matrix, then the values of a, b, c, are related with

If P is an orthogonal matrix and Q=PAP^(T) and x=P^(T)Q^(1000)P then x^(-1) is where A is involutary matrix.A b.I c.A^(1000)d . none of these

If matrix A=[(a,b),(c,d)] , then |A|^(-1) is equal to