Question

If $A \times A$, i.e., $A^{2} = 1,$ then $A$ is said to be an involutary matrix.

A) True

B) False

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Answer

Solution

The correct answer is Option A: True.

Recall the definition of an involutary matrix: a matrix $A$ is considered involutary if it satisfies two key conditions:

  1. $A$ must be a square matrix.
  2. The product $A \times A$ (or $A^2$) should equal the identity matrix $I$.

In this case, because it is stated that $A^2 = I$, we can deduce:

  • $A$ is a square matrix since we can compute $A^2$.
  • It satisfies the condition $A^2 = I$.

Thus, given these points, $A$ fulfills the criteria of being an involutary matrix, making the statement True.


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