<Dd> (I n) i j = δ i j . (\ displaystyle (I_ (n)) _ (ij) = \ delta _ (ij). \,) </Dd> <P> The identity matrix also has the property that, when it is the product of two square matrices, the matrices can be said to be the inverse of one another . </P> <P> The identity matrix of a given size is the only idempotent matrix of that size having full rank . That is, it is the only matrix such that (a) when multiplied by itself the result is itself, and (b) all of its rows, and all of its columns, are linearly independent . </P> <P> The principal square root of an identity matrix is itself, and this is its only positive definite square root . However, every identity matrix with at least two rows and columns has an infinitude of symmetric square roots . </P>

Rank of a unit identity matrix of order 4 is
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