If \(A\) is a \(3 \times 3\) non-zero matrix such that \(A^2 = 0\) then the determinant of \((I + A)^{50} - 50A\) is equal to

The determinant is $1$. Since $A^2=0$, the power reduces to $I+50A$, and subtracting $50A$ leaves the identity matrix. The value $3$ counts the diagonal entries and is the trace, whereas the determinant multiplies those entries.