Q.

Let A be a  2×2 matrix with rational entries such that  det(A22I2)=0 where det or  |.| represents determinant and  I2 is 2×2 identity matrix. Choose correct option(s).

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a

A99=249A

b

|A9|=29

c

A100=250A

d

|A40|=240

answer is B, C.

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Detailed Solution

det(A22I)=0        det(A2I)det(A+2I)=0
As A contains rational entries,  det(A2I)=det(A+2I)=0
So characteristics equation of A is  A22I2=0
A2n=2nI2,A2n+1=2nA&|A|=2.

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Let A be a  2×2 matrix with rational entries such that  det(A2−2I2)=0 where det or  |.| represents determinant and  I2 is 2×2 identity matrix. Choose correct option(s).