involutory Matrix

Question 1: How to prove that a matrix is involutory?

Answer:

Any square matrix “P” is said to be an involutory matrix if and only if P² = I or P = P^-1. So, to prove that a matrix is involutory, the matrix must satisfy the above condition.

Question 2: Define an involutory matrix.

Solution:

A square matrix is said to be an involutory matrix that, when multiplied by itself, gives an identity matrix of the same order.

Question 3: What is the relation between involutory and idempotent matrices?

Solution:

The following is the relationship between idempotent and involutory matrices: A square matrix “A” is said to be an involutory matrix if and only if A = ½ (B + I), where B is an idempotent matrix.

Question 4: Does the inverse of an involutory matrix exist?

Solution:

Yes, an involutory matrix is invertible. The inverse of an involutory matrix is equal to the original matrix itself.

Involutory Matrix is defined as the matrix that follows self inverse function i.e. the inverse of the Involutory matrix is the matrix itself. A matrix is defined as a rectangular array of numbers that are arranged in rows and columns. The size of a matrix can be determined by the number of rows and columns in it. A matrix is said to be an “m by n” matrix when it has “m” rows and “n” columns and is written as an “m × n” matrix. For example, a matrix of order “5 × 6” has five rows and six columns. We have different types of matrices, like rectangular, square, triangular, symmetric, singular, etc.