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A=[{:(a,b),(b,-a):}] and MA=A^(2m), m in...

`A=[{:(a,b),(b,-a):}]` and `MA=A^(2m)`, `m in N` for some matrix `M`, then which one of the following is correct ?

A

A. `M=[{:(a^(2m),b^(2m)),(b^(2m),-a^(2m)):}]`

B

B. `M=(a^(2)+b^(2))^(m)[{:(1,0),(0,1):}]`

C

C. `M=(a^(m)+b^(m))[{:(1,0),(0,1):}]`

D

D. `M=(a^(2)+b^(2))^(m-1)[{:(a,b),(b,-a):}]`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` Clearly option `(d)` satisfies the given conditions.
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