Question

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

Short answer

Therefore, the given condition is true.

Step-by-step solution

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.

To check whether the given condition is true or false.

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.