If A, B are square matrices of order 3, A is non-singular and AB = O, then B is a
(a) null matrix
(b) singular matrix
(c) unit-matrix
(d) non-singular matrix

Q. If

A

and

B

are square matrices of the same order and

A

is non-singular, then for a positive integer

n, (A^{- 1} B A)^{n}

is always equal to

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A and B are square matrices and A is non-singular matrix, (A−1BA)n,nϵI+ is equal to

The correct option is C A−1BnAFor n = 2 ⇒(A−1)(A−1BA)=A−1B2A(A−1B3A) and soon Thus (A−1BA)n=A−1BnA

A and B are square matrices and A is non-singular matrix, $(A^{- 1} B A)^{n}, n ϵ I^{+}$ is equal to

The correct option is C $A^{- 1} B^{n} A$
For n = 2 $\Rightarrow (A^{- 1}) (A^{- 1} B A) = A^{- 1} B^{2} A (A^{- 1} B^{3} A)$ and soon
Thus $(A^{- 1} B A)^{n} = A^{- 1} B^{n} A$