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

If A=[{:(3,x-1),(2x+3, x+2):}] is a symmetric matrix, then the value of x is

If A is a skew-symmetric matrix and n is odd positive integer, then A^n is a. a skew-symmetric matrix b. a symmetric matrix c. a diagonal matrix d. none of these

A is a square matrix such that A^(3)=I , then A^(-1) is equal to -

If Ais symmetric and B is skew-symmetric matrix, then which of the following is/are CORRECT ?

G is the centroid of triangle ABC and A_1 and B_1 are the midpoints of sides AB and AC , respectively. If Delta_1 is the area of quadrilateral G A_1A B_1 and Delta is the area of triangle ABC , then Delta/Delta_1 is equal to a. 3/2 b. 3 c. 1/3 d. none of these

If A is a skew symmetric matrix, then B=(I-A)(I+A)^(-1) is (where I is an identity matrix of same order as of A )

The inverse of a diagonal matrix is a. a diagonal matrix b. a skew symmetric matrix c. a symmetric matrix 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

If A is an invertible matrix, then (a d jdotA^(-1)) is equal to a. [a d jdot(A^(-1))] b. A/(d e tdotA) c. A d. (detA)A