Let `A and B` be `3xx3` matrtices of real numbers, where `A` is symmetric, `"B"` is skew-symmetric , and `(A+B)(A-B)=(A-B)(A+B)dot` If `(A B)^t=(-1)^k A B , where . (A B)^t` is the transpose of the mattix `A B ,` then find the possible values of `kdot`

Match the statement/expressions in Column I with the statements/expressions in Column II. Column I Column II The minimum value of (x^2+2x+4)/(x+2) is (p) 0 Let Aa n dBb e3x3 matrices of real numbers, where A is symmetric, B is skew symmetric, and (A+B)(A-B)=(A-B)(A+B) if (A B)^t=(-1)^kA B , where (A B)^t is the transpose of the matrix A B , then the possible values of k are (q) 1 Let a=(log)_3(log)_3 2. An integer k satisfying 1<2^(-k+3^((-1)))<2, must be less than (r) 2 In sintheta=cosvarphi, then the possible values of 1/pi(theta+-varphi-pi/2) are (s) 3

If (a+b)^2 = a^2 + 6a + 9 . Let's find,the possible value of b.

If A and B are symmetric matrices then

If A, B are square materices of same order and B is a skewsymmetric matrix, show that A^(T)BA is skew-symmetric.

Let A and B be two square matrices of the same size such that AB^(T)+BA^(T)=O . If A is a skew-symmetric matrix then BA is

Show that the matrix B'AB is symmetric or skew symmetric according as A is symmetric or skew symmetric.

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 and B are symmetric matrices of the same order, then show that AB is symmetric if and only if A and B commute i.e AB = BA .

Find the matrices A and B when A+B = 2B^(t) and 3A+2B=I_(3) where B^(t) denotes the transpose of B and I_(3) is the identity matrix of order 3.

If a - b = - 1 then find the value of (a^(3)-b^(3)+3ab+1)