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Q21E

Expert-verifiedFound in: Page 309

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.

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.

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

For $n\times n$ 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.

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