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Question
If A = `[(3, x),(0, 1)]` and B = `[(9, 16),(0, -y)]`, find x and y when A2 = B.
Solution
Given A = `[(3, x),(0, 1)]`, B = `[(9, 16),(0, -y)]` and A2 = B
Now, A2 = A × A
= `[(3, x),(0, 1)] xx [(3, x),(0, 1)]`
= `[(3 xx 3 + x xx 0, 1 xx x + x xx 1),(0 xx 3 + 1 xx 0, 0 xx x + 1 xx 1)]`
= `[(9 + 0, 3x + x),(0 + 0, 0 + 1)]`
= `[(9, 4x),(0, 1)]`
We have A2 = B
Two matrices are equal if each and every corresponding element is equal.
`=> [(9, 4x),(0, 1)] = [(9, 16), (0, -y)]`
`=>` 4x = 16 and 1 = –y
`=>` x = 4 and y = –1
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