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Transpose Conjugate

Prove the bel...

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Prove the below property of idemp. matrix If AB=A nad BA=B then A^n+B^n=A+B

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A

B

are square matrices of the same order such that

A B = B A

, then prove by induction that

{A B}^{n} = B^{n} A

. Further, prove that

{(A B)}^{n} = A^{n} B^{n}

n \in N

Q. If A and B are symmetric matrices then (AB + BA) is a matrix and (AB - BA) is a matrix.

m \times n

matrix and both AB and BA are defined prove that B should be

n \times m

Q. If A and B are skew symmetric matrices then (AB - BA) is a matrix and (AB + BA) is a matrix.

A, B

are two square matrices such that

A B = B; B A = A

n ϵ N

(A + B)^{n} =

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Transpose Conjugate

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