यदि `A = [(0" "1),(-1" "0)],B=[(i" "0),(0" "-i)]"` तथा `" "C = [(0" "-i),(-i" "0)]` है , तो निम्नलिखित में से कौन -सा एक सही नहीं है ?

Options

A. `A^(2) = B^(2)`
B. `B^(2) = C^(2)`
C. `AB = C `
D. `AB = BA `

Answer

D

Explanation

`:' A = [(0" " 1),(-1" "0)],B=[(i" "0),(0" "-i)]`
तथा ` C=[(0" "-i),(-i" "0)]`
`rArr AB = [(0" "1),(-1" "0)][(i" "0),(0" "-i)]=[(0" "-i),(-i" "0)]=C`
` :. AB = C`
` BA = [(i" "0),(0" "-i)][(0" "1),(-1" "0)]=[(0" "i)(i" "0)]`
` rArr AB ne BA`
`A^(2) = [(0" "1),(-1" "0)][(0" "1),(-1" "0)]=[(-1" "0),(0" "-1)]`
`B^(2) =[(i" "0),(0" "-i)]xx[(i" "0),(0" "-i)]=[(-1" "0),(0" "-1)]`
` rArr A^(2) = B^(2)`
` C^(2) = [(0" "-i),(-i" "0)][(0" "-i),(-i" "0)]`
` = [(-1" "0),(0" "-1)] rArr B^(2) = C^(2)`