If A is a nonsingular matrix such that `A A^(T)=A^(T)A` and `B=A^(-1) A^(T)`, then matrix B is

If A is a 3xx3 non -singular matrix such that "AA"^(T)=A^(T)A "and" B=A^(-1)A^(T), "then" BB^(T) =

If A is a non-singular matrix such that A^(-1)=[(5,3),(-2,-1)], "then" (A^(T))^(-1) =

If A is a non singular matrix such that A^(-1)=[[7,-2],[-3,1]] then (A^(T))^(-1) is :

If A and B are two non-singular matrices of order 3 such that A A^(T)=2I and A^(-1)=A^(T)-A . Adj. (2B^(-1)) , then det. (B) is equal to

If A is a 3xx4 matrix and B is a matrix such that both A^(T) B and BA^(T) are defined, what is the order of the matrix B?

If A is a square matrix of order less than 4 such that |A-A^(T)| ne 0 and B= adj. (A), then adj. (B^(2)A^(-1) B^(-1) A) is

Let a be square matrix. Then prove that A A^(T) and A^(T) A are symmetric matrices.