Question

What is a unit matrix?

Answer 1

Hint: In mathematics Matrix is the set of numbers which are arranged in the rows and the columns so as to form the rectangular array. The numbers arranged in the matrix are called the elements or the entries of the matrix.

Complete step-by-step solution:
The dimensions of the matrix suggest its size , the number of the rows and the number of columns of the matrix that is its order.
Let us take an example:
\[A = \left[ {\begin{array}{*{20}{c}}
  1&3 \\
  4&5
\end{array}} \right]\]
The above given matrix has two rows and the three columns and its dimensions as $2 \times 2$ and the matrix is pronounced as of the order “two by two”.
Now, the unit matrix can be defined as the every $n \times n$ matrix which is made up of all zeros except for the elements of the main diagonal which are all ones.
For example: $\left[ {\begin{array}{*{20}{c}}
  1&0 \\
  0&1
\end{array}} \right]$
Unit matrix is denoted by: ${I_n}$ where “n” represents the size of the matrix.
In linear algebra, the unit matrix works as the number one in the normal algebra so if you multiply a matrix by the unit matrix to get the same initial matrix.

Note: Don’t be confused between the determinants and the matrices. Determinant is the square matrix with the same number of rows and columns whereas, the matrix is the rectangular grid of numbers and number of rows and the columns may not be the same.