A skew-symmetric matrix `A` satisfies the relation `A^2+I=O ,w h e r e I` is a unit matrix then `A` is a. idempotent b. orthogonal c. of even order d. odd order

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 )

If A is a skew symmetric matrix of order n and C is a column matrix of order nxx1 ,then C^(T)AC is

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

If A is an idempotent matrix satisfying, (I-0. 4 A)^(-1)=I-alphaA ,w h e r eI is the unit matrix of the name order as that of A , then th value of |9alpha| is equal to ________.

If M is a 3xx3 matrix, where det M=1a n dM M^T=1,w h e r eI is an identity matrix, prove theat det (M-I)=0.

If f(x) is an even function and satisfies the relation x^2dotf(x)-2f(1/x)=g(x),w h e r eg(x) is an odd function, then find the value of f(5)dot

If A is an idempotent matrix satisfying (I-0.4A)^(-1)=I-alphaA where I is the unit matrix of the same order as that of A then the value of alpha is

Matrix A such that A^2=2A-I ,w h e r eI is the identity matrix, the for ngeq2. A^n is equal to 2^(n-1)A-(n-1)l b. 2^(n-1)A-I c. n A-(n-1)l d. n A-I

Let A be a square matrix of order 3 satisfies the relation A^(3)-6A^(2)+7A-8I=O and B=A-2I . Also, det. A=8 , then

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