Question

(B-C)^2=(C-B)^2, Where B and C are

(n x n) in matrices.Is it true or false.

Answer 1

Let P=(B-C), and Q=(C-B)

We understand from the definition of subtraction of matrices that P=-Q, or
p(i,j)=-q(i,j).

Let P=
|2 0|
|3 1|
and Q=
|-2 0|
|-3 -1|
and compare P^2 and Q^2 to make your conclusion.