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

If for the matrix A ,\ A^3=I , then A^(-1)= (a) A^2 (b) A^3 (c) A (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

If A is an invertible matrix then det(A^-1) is equal to (A) 1 (B) 1/|A| (C) |A| (D) none of these

For any set A ,(A ')' is equal to a. A ' b. A c. varphi 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.

(-A)^(-1) is always equal to (where A is nth-order square matrix) a. (-A)^(-1) b. -A^(-1) c. (-1)^nA^(-1) d. none of these

If A^3=O ,t h e nI+A+A^2 equals a. I-A b. (I+A^1)^(-1) c. (I-A)^(-1) 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

If both A-1/2Ia n dA+1/2 are orthogonal matices, then (a) A is orthogonal (b) A is skew-symmetric matrix of even order (c) A^2=3/4I (d)none of these