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If `A =[(4, 2),(1,1)]` Find (A - 2i)(A - 3i) - ICSE Class 10 - Mathematics

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Question

If `A =[(4, 2),(1,1)]` Find (A - 2I)(A - 3I)

Solution

`A - 2I = [(4, 2),(1, 1)] - 2[(1, 0),(0, 1)] = [(4, 2),(1,1)] - [(2, 0),(0, 2)] = [(2,2),(1, -1)]`

`A - 3I = [(4, 2),(1,1)] - 3[(1, 0),(0, 1)] = [(4, 2),(1, 1)] - [(3, 0),(0, 3)] = [(1, 2),(1, -2)]`

`(A- 2I)(A- 3I) = [(2,2),(1, -1)][(1, 2),(1, -2)]`

`=[(2 + 2, 4 - 4),(1 - 1, 2 + 2)]`

`= [(4,0),(0, 4)]`

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Solution If `A =[(4, 2),(1,1)]` Find (A - 2i)(A - 3i) Concept: Matrices Examples.
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