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If A is a matrix of order mxx m such tha...

If A is a matrix of order `mxx m` such that
`A^(2) +A + 2I = O`, then

A

A is non-singular

B

A is symmetric

C

`abs(A)ne 0 `

D

`A^(-1) = 1/2(A+I)`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
Here, `A(A + I) = -2I` ...(i)
` rArr abs(A(A +I))=abs(-2I) = (-2)^(m)ne 0 `
Thus, `abs(A) ne 0,`
also, `I= -1/2 A(A+I)` [from Eq. (i)]
`therefore A^(-1) = -1/2 (A + I)`
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