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If A=[(ab,b^2),(-a^2,-a b)] , show that ...

If `A=[(ab,b^2),(-a^2,-a b)]` , show that `A^2=0` .

Text Solution

Verified by Experts

Given,
`A=[(ab,b^2),(-a^2,-a b)]`
so,
`A^2=[(ab,b^2),(-a^2,-a b)]xx[(ab,b^2),(-a^2,-a b)]`
`=[((ab)^2-(ab)^2,(ab)^3-(ab)^3),(-a^3b+a^3b,-(ab)^2+(ab)^2)]`
`=[(0,0),(0,0)]`
Hence `A^2=0`
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