यदि `A = [(omega" "0),(0" "omega)]`, जहाँ `omega`इकाई का घनमूल है , तो `A^(100)` किसके बराबर है ?

Options

A. A
B. `-A`
C. शून्य आव्यूह
D. तत्समक आव्यूह

Answer

A

Explanation

दिया है , `A=[(omega" "0),(0" " omega)]`
अब ,`A^(2) = [(omega" "0),(0" "omega)][(omega" "0),(0" "omega)]=[(omega^(2)" "0),(0" " omega^(2))]`
`A^(3) = [(omega^(2)" "0),(0" "omega^(2))][(omega" "0),(0" "omega)]=[(omega^(3)" "0),(0" "omega^(3))]`
` =[(1" "0),(0" "1)]=I" "[:' omega^(3) =1]`
इसी प्रकार , `A^(100)=(A^(3))^(33)*A=(I)^(33)*A`
` = I*A=A`