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Let \( A \) and \( B \) are two matrices such that \( A B=B A \), then for every \( n \in \mathbf{N} \),
(a) \( A^{n} B=B A^{n} \)
(b) \( (A B)^{n}=A^{n} B^{n} \)
(c) \( (A+B)^{n}={ }^{n} C_{0} A^{n}+{ }^{n} C_{1} A^{n-1} B+ \)
\[
{ }^{n} C_{2} A^{n-2} B+\ldots+{ }^{n} C_{n} B^{n} .
\]
(d) \( A^{2 n}-B^{2 n}=\left(A^{n}-B^{n}\right)\left(A^{n}+B^{n}\right) \)
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