If `A` is a matrix such that `A^2+A+2I=Odot,` the which of the following is/are true? (a) A is non-singular (b) A is symmetric (c) A cannot be skew-symmetric (d) `A^(-1)=-1/2(A+I)`

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

Express the following matrices as the sum of a symmetric and a skew symmetric matrix: [(1,5),(-1,2)]

Let Aa n dB be two nonsingular square matrices, A^T a n dB^T are the transpose matrices of Aa n dB , respectively, then which of the following options are correct? (correct option may be more than one) (a) . B^T A B is symmetric matrix (b) . if A is symmetric B^T A B is symmetric matrix (c) . if B is symmetric B^T A B is skew-symmetric matrix for every matrix A (d) . B^T A B is skew-symmetric matrix if A is skew-symmetric

If alpha,beta,gamma are three real numbers and A=[(1,"cos"(alpha-beta),"cos"(alpha-gamma)),(cos(beta-alpha),1,"cos"(beta-gamma)),("cos"(gamma-alpha),"cos"(gamma-beta),1)] , then which of following is/are true? a. A is singular b. A is symmetric c. A is orthogonal d. A is not invertible

If Aa n dB are symmetric and commute, then which of the following is/are symmetric? A^(-1)B b. A B^(-1) c. A^(-1)B^(-1) d. none of these

If A = [(4,1),(7,2)] find a matrix B such that AB = I where I is the unit matrix of order 2.

Let A be a square matrix. Then prove that (i) A + A^T is a symmetric matrix and, (ii) A -A^T is a skew-symmetric matrix

If A is a matrix of order n such that A^(T)A=I and X is any matrix such that X=(A+I)^(-1) (A-I) , then show that X is skew symmetric matrix.

Let A=a_0 be a matrix of order 3, where a_(i j)=x ; ifi=j ,x in R, 1 if|i-j|=1, 0;ot h e r w i s e then when of the following Hold (s) good: for x=2 , (a) A is a diagonal matrix (b) A is a symmetric matrix for x=2 , (c) det A has the value equal to 6 (d) Let f(x)= , det A , then the function f(x) has both the maxima and minima.

If A is a non-singular matrix of order nxxn such that 3ABA^(-1)+A=2A^(-1)BA , then