Question

What is the determinant of an identity matrix?

Answer 1

The ith column of an identity matrix is the unit vector ei. It follows that the determinant of the identity matrix is 1 and the trace is n.

Answer 2

Answer:

An identity matrix has a determinant of zero. A zero-dimensional matrix has a determinant of one.

Step-by-step explanation:

• A square matrix called an identity matrix is one in which all of the primary diagonal members are one and all other components are zero.
• It is also known as an elementary matrix or a unit matrix.
• It is denoted as In or simply by I, where n denotes the square matrix's size.
• In identity matrix the outcome is itself when it is multiplied by itself.
• Its columns and rows are all linearly independent.
• The identity matrix serves as the equivalent object to the unit in numerical algebra.

Identity matrix can be denoted as

$I_{1} = 1$

$I_{2} = \left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

$I_{3} = \left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$

• The specified matrix's elements remain unchanged.
• The principal diagonal elements of the identity matrix are ones, and the remaining elements are zeros.

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