Rapid Revision Bullets

det(kA) = $k^n$ det(A) -- #1 trap, n is the order
det( $A^T$ ) = det(A), det(AB) = det(A)det(B)
adj(A) = TRANSPOSE of cofactor matrix
A * adj(A) = det(A) * I
det(adj(A)) = det(A)^(n-1)
adj(adj(A)) = det(A)^(n-2) * A
A^(-1) = adj $\frac{A}{det}$ (A), exists only when det != 0
(AB)^(-1) = B^(-1)A^(-1) -- reversal law
Cayley-Hamilton (2x2): $A^2$ - (tr A)A + (det A)I = O
Skew-symmetric odd order: det = 0 always
Vandermonde det = (a-b)(b-c)(c-a)
D != 0: unique solution (Cramer's Rule)
D = 0, all $D_i$ = 0: infinite solutions
D = 0, some $D_i$ != 0: no solution
Homogeneous: non-trivial iff det = 0
AB = O does NOT mean A = O or B = O
Matrix multiplication: associative but NOT commutative
Orthogonal: A^(-1) = $A^T$ , det = +/-1
Idempotent: eigenvalues 0 or 1, tr = rank
For triangular matrices: det = product of diagonal entries