Question:

Let A be a square matrix of order 3 whose all entries are 1 and let I3I_3 be the identity matrix of order 3. Then the matrix A−3I3A - 3I_3 is

Updated On: Apr 27, 2024
  • invertible
  • orthogonal
  • non-invertible
  • real Skew Symmetric matrix
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The Correct Option is A

Solution and Explanation

A−3I3=[011101110],∣A−3I3∣≠0A - 3I_{3} = \begin{bmatrix}0&1&1\\ 1&0&1\\ 1&1&0\end{bmatrix}, \left|A - 3I_{3}\right| \ne 0
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Concepts Used:

Matrices

Matrix:

A matrix is a rectangular array of numbers, variables, symbols, or expressions that are defined for the operations like subtraction, addition, and multiplications. The size of a matrix is determined by the number of rows and columns in the matrix.

The basic operations that can be performed on matrices are:

  1. Addition of Matrices - The addition of matrices addition can only be possible if the number of rows and columns of both the matrices are the same.
  2. Subtraction of Matrices - Matrices subtraction is also possible only if the number of rows and columns of both the matrices are the same.
  3. Scalar Multiplication - The product of a matrix A with any number 'c' is obtained by multiplying every entry of the matrix A by c, is called scalar multiplication. 
  4. Multiplication of Matrices - Matrices multiplication is defined only if the number of columns in the first matrix and rows in the second matrix are equal. 
  5. Transpose of Matrices - Interchanging of rows and columns is known as the transpose of matrices.