Let A be an orthogonal matrix, and B is a matrix such that `AB=BA`, then show that `AB^(T)=B^(T)A`.

If A is any mxn matrix and B is a matrix such that AB and BA are both defined, then B is a matrix of order

Show that , if A and B are square matrices such that AB=BA, then (A+B)^(2)=A^(2)+2AB+B^(2) .

Let B is an invertible square matrix and B is the adjoint of matrix A such that AB=B^(T) . Then

If A and B are non-singular symmetric matrices such that AB=BA , then prove that A^(-1) B^(-1) is symmetric matrix.

Let A and B are two matrices such that AB = BA, then for every n in N

If A is a 3xx3 matrix and B is a matrix such that A^TB and BA^(T) are both defined, then order of B is

If A is 2xx3 matrix and B is a matrix such that A^T\ B and B A^T both are defined, then what is the order of B ?

The number of nxxn matrix A and B such that AB - BA = I is. . .

If A is matrix of order mxxn and B is a matrix such that AB' and B'A are both defined , then order of matrix B is

A is even ordered non singular symmetric matrix and B is even ordered non singular skew symmetric matrix such that AB = BA, then A^3B^3(B'A)^(-1)(A^(-1)B^(-1))' AB is equal to :