I was given this question in one of my interviews. I have tried a lot even after that but I am not able to get a hold of it. Can anybody help me with this.
Function $f$ has the following properties
- $f:$ Square Matrix -> Real
- $f(I_n) = 1$ // Identity Matrix of size n maps to one : independent of n
- If $A$ and $B$ both are square matrices of same size then $f(AB) = f(BA)$
- If $A$ and $B$ both are square matrices of same size then $f(mA+nB) = mf(A) + nf(B)$
Describe the family of functions $f$ that satisfies the above criteria.
The only property I was able to obtain was that $f(-A) = -f(A)$
Thanks