For any unit matrix I

The correct option is I² = I.

Let's understand the properties of a unit matrix (also known as an identity matrix, denoted as $I$) to see why this option is correct.

A unit matrix $I$ of order $n$ is a square matrix in which all the elements of the principal diagonal are equal to 1, and all other elements are 0.
For example, a $2\times 2$ unit matrix is:

$$I=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$$

One of the fundamental properties of the unit matrix is that it acts as the multiplicative identity in matrix algebra. This means multiplying any matrix by $I$ (as long as the dimensions are compatible) leaves the matrix unchanged.

Therefore, if we multiply the unit matrix $I$ by itself, we get:

$$I^2=I·I=I$$

This confirms that $I^2=I$ is a true statement for any unit matrix.

To verify why the other options are incorrect:
The determinant of any unit matrix is always equal to 1 (i.e., $\left|I\right|=1$). Therefore, the statements $\left|I\right|=0$, $\left|I\right|=2$, and $\left|I\right|=5$ are incorrect.