If `A` is non-diagonal involuntary matrix, then `A=I=O` b. `A+I=O` c. `A=I` is nonzero singular d. none of these

If B is an idempotent matrix, and A=I-B , then

If A is a singular matrix, then adj A is a. singular b. non singular c. symmetric d. not defined

If Z is an idempotent matrix, then (I+Z)^n I+2^n Z b. I+(2^n-1)Z c. I-(2^n-1)Z d. none of these

If A is a square matrix such that A^(3)=I , then prove that A is non-singular

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 C is skew-symmetric matrix of order na n dXi snxx1 column matrix, then X^T C X is a. singular b. non-singular c. invertible d. non invertible

If P is non-singular matrix, then value of adj(P^(-1)) in terms of P is (A) P/|P| (B) P|P| (C) P (D) none of these

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

In which of the following type of matrix inverse does not exist always? a. idempotent b. orthogonal c. involuntary d. none of these

If vec A O+ vec O B= vec B O+ vec O C , then A ,Bn a dC are (where O is the origin) a. coplanar b. collinear c. non-collinear d. none of these