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Q21E

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Found in: Page 309

### Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

# If all the entries of a square matrix are 1 or 0, then must be 1, 0, or -1.

Therefore, the given condition is true.

See the step by step solution

## Step 1: Orthogonal Matrix Definition.

A square matrix with real numbers or elements is said to be an orthogonal matrix, if its transpose is equal to its inverse matrix.

Or we can say, when the product of a square matrix and its transpose gives an identity matrix, then the square matrix is known as an orthogonal matrix.

## Step 2: To check whether the given condition is true or false.

For, $2×2$ matrices whose entries are 0 and 1 , the determinant can only be -1, 0 , or 1.

For $n×n$ matrices, where $n>2$, this applies using the Laplace expansion.

Therefore,

$detA=-1,0,1$.

Therefore, the given condition satisfied and the given statement is true.