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# If $I$ is a unit matrix of order $2 \times 2$ then write down the value of $\left| I \right|$.

Last updated date: 25th Mar 2023
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Hint: Here the unit matrix is every $n \times n$ square matrix made of all zeros except for the elements of the main diagonal that are all ones. And the determinant is a scalar value that can be computed from the elements of a square matrix and encodes certain properties of the linear transformation described by the matrix. With these basic concepts we can solve this problem easily.

Given $I$ is a unit matrix of order $2 \times 2$
i.e., $I = \left[ {\begin{array}{*{20}{c}} 1&0 \\ 0&1 \end{array}} \right]$
The determinant of $I$ is given by
$\left| I \right| = \left| {\begin{array}{*{20}{c}} 1&0 \\ 0&1 \end{array}} \right|$
We know that the determinant of matrix $\left| A \right| = \left| {\begin{array}{*{20}{c}} a&b \\ c&d \end{array}} \right|$ is $ad - bc$.
$\left| I \right| = \left( 1 \right)\left( 1 \right) - \left( 0 \right)\left( 0 \right) = 1 - 0 = 1$
Thus, the value of $\left| I \right| = 1$.
Note: In this problem “$\left| {} \right|$” denotes the determinant of a matrix. A unit matrix is always a square matrix and the number of rows and number of columns are always equal. The determinant of a unitary matrix is always equal to 1.