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Husk, (削除) 12 11 (削除ここまで) 10 bytes

≡1 ́Ṫ§^*=l·L

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Explanation

≡1 ́Ṫ§^*=l·L Input is a k×ばつk array A.
 L The length, k.
 l· The range [0,1..k-1].
 ́Ṫ Outer product with itself by this function:
 Arguments are two numbers x and y.
 = Equality of x and y
 §^ to the power of
 * x times y.
≡1 Does the result have the same shape and distribution of truthy values as A?

The idea is that Husk defines 0 to the power of 0 as 1, so the outer product has 1s on the first row and column. Also, 1 to the power of any number is 1, so the outer product has 1s on the diagonal. Other entries are 0 to the power of some positive number, which is 0. This gives a binary arrowhead matrix, which we compare to the input with ≡.