Is their finite such matrices?

Let $A= \begin{bmatrix}{a} && {0} && {0} && {0} \\ {0} && {b} && {0} && {0} \\ {0} && {0} && {c} && {0} \\ {0} && {0} && {0} && {d} \\ \end{bmatrix}$ $A^2=AA= \begin{bmatrix}{a^2} && {0} && {0} && {0} \\ {0} && {b^2} && {0} && {0} \\ {0} && {0} && {c^2} && {0} \\ {0} && {0} && {0} && {d^2} \\ \end{bmatrix}$ $A=A^2 \Rightarrow a=a^2,b=b^2,c=c^2,d=d^2$ $\color{#3D99F6}{ \Rightarrow \text{ a,b,c,d}=0 \space or\space 1}$ Therefore total number of matrices= $2\times2\times2\times2=16$ But this also contains the Zero matrix. Therefore answer= $\color{#D61F06}{16-1=15}$