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1.Show that B satisfies the equation (B-pI)(B-qI) = 0

2.Hence, or otherwise, show that B^{-1}= 0.5(3I - B)

In these kind of questions I don't know what they are testing me for! Let's take the first one as an example: The only skill they can possibly try to asses is whether I know how to multiply the matrix I by values I found previously (p and q). Other than that, all I can do to "answer" the question is performing the multiplication and showing it equals zero?

For the second one it is even worst... I know how to calculate the inverse of B and when I do it does in fact equal 0.5(3I - B), but, what should I put on paper? Calculate the inverse the regular way and then perform 0.5(3I - B) and show the results are equal?

I'm not sure if I was able to convey my doubt clearly... If the problem is due to lack of information in questions 1 and 2 I can add more information or rephrase my query.

Thanks,

Peter G.

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# Hence show that (Matrices)

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