A matrices question: Suppose A = 2A^(-1)....

[Guest]

Suppose A = 2A^-1(inverse)
Simplify (A- I) (A + 3I) where r and s are members of the set of Real Numbers and I is the identity matrix.

Leave answer in the form r(A) + s(I).

thank you in advance

 

[daon]

(A-I)(A+3I) = (A-I)(A) + (A-I)(3I) = AA +2A - 3I

By your given, AA+2A-3I = A(2A^(-1)) + 2A - 3I = 2AA^(-1) + 2A - 3I = 2I + 2A - 3I = 2A - I

or

(2)A + (-1)I