Proof: Matrix A^-1 = -(1/3)((A^2) -2A -4I)

[forty]

Show that A^-1 = -(1/3)((A^2) -2A -4I)

In the question it gives you matrix A, so i presume the question just wants you to evaluate the right hand side.

But can this be done without just subbing in the matrix given?

A = [1 0 1;2 3 4;-1 0 -2]

 

[HallsofIvy]

What would evaluating the right side tell you? If the equation is correct, it should give you A^-1. Have you already found that inverse? Simpler would be to evaluate the right side, then multiply that by A.

But to answer your question, yes, that is exactly what "evaluate" means. If you were asked to evaluate the (numerical) polynomial -(1/3)(x²- 2x- 4) for x= 2, you would replace x by 2 and do the arithmetic. Same thing here.

 

[forty]

love you as always :)