# If A x A, i.e., A^2 = 1, then A is said to be an involutary matrix. A) True B) False

## 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:

- $A$ must be a
**square matrix**. - 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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