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*n*x

*n*matrix which satisfies the equation

A

^{3}- 2A

^{2}+ 3A - I = 0

Show that the

*n*x

*n*matrix B defined by the equation B = A

^{2}- 2A +3I is invertible and find its inverse.

Does anyone have any idea what this type of problem is called, and what steps you take to solve it?