Let a be a matrix of order `2xx2` such that `A^(2)=O`. `A^(2)-(a+d)A+(ad-bc)I` is equal to
Let a be a matrix of order `2xx2` such that `A^(2)=O`.
`A^(2)-(a+d)A+(ad-bc)I` is equal to
A. `I`
B. `O`
C. `-I`
D. none of these
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Correct Answer - B
Let
`A=[(a,b),(c,d)]`
`implies A^(2)-(a+d)A+(ad-bc)I`
`=[(a,b),(c,d)][(a,b),(c,d)]-(a+d)[(a,b),(c,d)]+(ad-bc)[(1,0),(0,1)]`
`=[(a^(2)+bc,ab+bd),(ac+cd,bc+d^(2))]-[(a^(2)+ad,ab+bd),(ac+cd,bc+d^(2))]+[(a^(2)+ad,ab+bd),(ac+cd,ad+d^(2))]`
`=O`
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