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## Homework Statement

Let {a,b,c} be any basis set. Then the corresponding reciprocal {a*,b*,c*} is defined by

a*=b x c/[a,b,c] , b*=c x a/[a,b,c], c*=a x b/[a,b,c]

If {i,j,k} is standard basis, show that {i*,j*,k*}={i,j,k}

## Homework Equations

## The Attempt at a Solution

I have no idea how to start this problem. I know the standard basis is just the identity matrix. But thats all I know. I don't know what {i*,j*,k*} is supposed to symbolized. Is it the inverse of {i,j,k}?