Question

Why do we use \[I\] in math?

Answer 1

Hint: The upper case of the alphabet I is used to denote a identity matrix. The lower case of the alphabet I is used to denote \[\sqrt{-1}\].

Complete step by step solution:
Complex number: Every complex number can be represented in the form \[a + bi\] , where a and b are real numbers. A complex number is a part of a number system that extends the real numbers with a particular element denoted by \[i\] and it is known as the imaginary unit, satisfying the equation \[{i^2} = - 1\] .
For complex numbers, \[i\] is denoted as a complex number. e.g., \[a + bi\] , where \[{i^2} = - 1\] and \[{i^3} = - i\]

Matrix: A matrix is a rectangular array or table containing rows and columns of numbers, symbols, or expressions that are used to represent a mathematical object or an attribute of one. \[\left[ {\begin{array}{*{20}{c}}1&2\\3&4\end{array}} \right]\] is a matrix having two rows and two columns, for instance.
Every matrix has \[m\] rows and \[n\] columns.
We can denote a matrix by \[{A_{m \times n}}\] .
In matrix \[I\] denoted as an identity matrix. If we take a \[2 \times 2\] matrix then it is shown as
\[{I_{2 \times 2}} = \left[ {\begin{array}{*{20}{c}}1&0\\0&1\end{array}} \right]\]
\[{I_{3 \times 3}} = \left[ {\begin{array}{*{20}{c}}1&0&0\\0&1&0\\0&0&1\end{array}} \right]\]
…..
\[{I_{m \times m}} = \left[ {\begin{array}{*{20}{c}}1& \cdots &0\\ \vdots & \vdots & \vdots \\0& \cdots &1\end{array}} \right]\]

Note: Students need to take care about the row and column of the identity matrix. In the identity matrix, the values of diagonal entries are 1 and rest entries are 0. Remember an identity matrix is always a square matrix.