Let $A$ be a $10\times10$ matrix such that $A^{5}$ is a null matrix, and let $I$ be the $10\times10$ identity matrix. The determinant of $\text{A+I}$ is ___________________.

ans 1

A is null matrix

then A^5=A

A+I=I

where is I identity matrix

determinant of (A+I)=determinant(I)

determinant of I=1(ans)
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