(T/F) An $n \times n$ determinant is defined by determinants of $(n-1) \times(n-1)$ submatrices.
(A) True
(B) False

Answer

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Answer

Since the Laplace expansion involves calculating determinants of (n-1) x (n-1) submatrices, the statement is true. $\boxed{\text{(A) True}}$

Steps

Step 1 ：Calculate the determinant of a 3x3 matrix using the Laplace expansion: $\det(A) = a_{11}C_{11} - a_{12}C_{12} + a_{13}C_{13}$

Step 2 ：Since the Laplace expansion involves calculating determinants of (n-1) x (n-1) submatrices, the statement is true. $\boxed{\text{(A) True}}$