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Let A and B be 4 * 4 matrices with real entry, such that they satisfy the equation $A^2-2B+I=0$ and $ B^2–2A+I=0$. Given that |A-B| is non zero, find the value of det|A+B|.

I subtracted both the equations So i got $ A^2-B^2$ = 2(B-A) now if i can say A and B commute then i will be able to further solve. Can i say A and B commmute?

maveric
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2 Answers2

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Make a power four eqn in A. $(A-I)^2 (A^2+3A+5I) =0$. Answer come s out to be 16

Math_centric
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    Your formula $(A-I)^2(A^2+3A+5I)=0$ is false and your answer also. –  May 08 '20 at 22:20
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$B$ commutes with $A$ because $B$ is a polynomial in $A$.

lhf
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