[If A and B are square matrices of the same order, then det(AB) = det(A)det(B)]
∴ det(A × A−1) = det(A) × det(A−1)
⇒ det(I) = det(A) × det(A−1) = 1
∴ det(A−1) = (det(A))-1
∴ k = -1
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