Let `Ad nB` be `3xx3` matrtices of ral 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 ,w h e r e(A B)^t` is the transpose of the mattix `A B ,` then find the possible values of `kdot`

Let A and B are 3xx3 matrices with real number entries, where A is symmetric, B is skew - symmetric and (A+B)(A-B)=(A-B)(A+B) . If (AB)^(T)=(-1)^(k)AB , then the sum of all possible integral value of k in [2, 10] is equal to (where A^(T) represent transpose of matrix A)

If A is skew-symmetric and B=(I-A)^(-1)(I+A), then B is

Let A and B be any two 3xx3 matrices . If A is symmetric and B is skew -symmetric then the matrix AB-BA is :

If A is a symmetric and B skew symmetric matrix and (A+B) is non-singular and C=(A+B)^(-1)(A-B), then prove that

If A is symmetric and B skew- symmetric matrix and A + B is non-singular and C= (A+B) ^(-1) (A-B) , C^(T)(A+B)C equals to

If A is symmetric and B skew- symmetric matrix and A + B is non-singular and C= (A+B) ^(-1) (A-B) C^(T) AC equals to

Let A and B be symmetric matrices of same order. Then A+B is a symmetric matrix, AB-BA is a skew symmetric matrix and AB+BA is a symmetric matrix

If A^(T), B^(T) are transpose of the square matrices A, B respectively, then (AB)^(T)=