The left-hand side becomes A*I_n - B*0_n,n = A, correct? How can A = det(A) just from the information given?
2026-04-25 00:53:31.1777078411
Matrix Determinants Equivalence
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Hint: Use a cofactor expansion along the diagonal of $I$. Look at this small example to see the pattern: $$ \det\left[\begin{array}{ccccc} 1 & & & 2 & 3\\ & 1 & & 4 & 5\\ & & 1 & 6 & 7\\ & & & 8 & 9\\ & & & 10 & 11 \end{array}\right]=\det\left[\begin{array}{cccc} 1 & & 4 & 5\\ & 1 & 6 & 7\\ & & 8 & 9\\ & & 10 & 11 \end{array}\right]=\det\left[\begin{array}{ccc} 1 & 6 & 7\\ & 8 & 9\\ & 10 & 11 \end{array}\right]=\det\left[\begin{array}{cc} 8 & 9\\ 10 & 11 \end{array}\right] $$