(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. $(A) True$

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. $(A) True$