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The matrix A=[-5-8 0 3 5 0 1 2-] is a. i...

The matrix `A=[-5-8 0 3 5 0 1 2-]` is a. idempotent matrix b. involutory matrix c. nilpotent matrix d. none of these

A

idempotent matrix

B

involutory matrix

C

nilpotent matrix

D

none of these

Text Solution

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The correct Answer is:
involutory matrix
`A^(2)=AxxA[(-5,-8,0),(3,5,0),(1,2,-1)]xx[(-5,-8,0),(3,5,0),(1,2,-1)]`
`=[(25-24+0,40-40+0,0+0+0),(-15+15+0,-24+25+0,0+0+0),(-5+6-1,-8+10-2,0+0+1)]`
`=[(1,0,0),(0,1,0),(0,0,1)]`
Hence, the given matrix a is involutory.
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