(B-C)^2=(C-B)^2 ,where B and C are
(n x n) matrices.what is the answer, it is true or false
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You can simplify the problem to:
does A^2=(-A)^2?
The answer lies in how each element of A^2 is calculated, namely as the product of two elements of A.
To determine whether the equation (B - C)^2 = (C - B)^2 is true or false, we can expand both sides of the equation and simplify.
The expression (B - C)^2 can be expanded as (B - C)(B - C), which results in B^2 - BC - CB + C^2.
Similarly, the expression (C - B)^2 can be expanded as (C - B)(C - B), which results in C^2 - CB - BC + B^2.
Comparing both expansions, we can observe that both sides of the equation are equal:
B^2 - BC - CB + C^2 = C^2 - CB - BC + B^2.
By rearranging the terms, we notice that all the terms cancel each other out:
B^2 - BC - CB + C^2 - C^2 + CB + BC - B^2 = 0.
Thus, the equation simplifies to 0 = 0, which is always true for any matrices B and C of size (n x n).
Therefore, the equation (B - C)^2 = (C - B)^2 is true for any (n x n) matrices B and C.