No solutions with code please, I need logic and math

$4\mathrm{.}14.$ Your task is to compute the S$-$Box, i$.$e$.,$ the ByteSub, values for the input bytes $29,$ F$3$ and $01,$ where each byte is given in hexadecimal notation.

$1.$ First, look up the inverses using Table $4\mathrm{.}2$ to obtain values $\backslash ($ B$^\{\backslash$prime$\}\backslash ).$ Now, perform the affine mapping by computing the matrix$-$vector multiplication and addition.

$2.$ Verify your result using the S$-$Box Table $4\mathrm{.}3.$

$3.$ What is the value of $\backslash ($ S$(0)\backslash )?$