If `A` is any `mxxn` such that `A B` and `B A` are both defined show that `B` is an `nxxm` matrix.

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

If A is a matrix of order mxxn and B is a matrix such that A B^T and B^T A are both defined, then the order of matrix B is (a) mxxn (b) nxxn (c) nxxm (d) mxxm

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 ,\ B are two matrices such that A B and A+B are both defined; show that A ,\ B are square matrices of the same order.

If A is 3xx4 matrix and B is a matrix such that A^T B and B A^T are both defined. Then, B is of the type (a) 3xx4 (b) 3xx3 (c) 4xx4 (d) 4xx3

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 ?

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

Show that A' A and A A' are both symmetric matrices for any matrix A.

Let A and B be two matrices such that the order of A is 5xx7 . If A^(T)B and BA^(T) are both defined, then (where A^(T) is the transpose of matrix A)

Show that the binary operation * on Z defined by a*b= 3a+7b is not commutative.