If A is an nxn matrix then rank A = n iff det A is not 0

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An nxn matrix A is non singular iff rank A = n An nxn matrix A is non singular iff rank A = n
Corollary to an nxn matrix A is non singular iff rank (A) = n Corollary to an nxn matrix A is non singular iff rank (A) = n
LA44 A invertible iff Det(A) not zero; Det(AB) = Det(A) Det(B) LA44 A invertible iff Det(A) not zero; Det(AB) = Det(A) Det(B)
Let A be an nxn matrix whose entries are all 1 Let A be an nxn matrix whose entries are all 1's Then det(A-nI)=0
Proof: If the inverse of A exists, the the determinant of A cannot be zero. Proof: If the inverse of A exists, the the determinant of A cannot be zero.
MOST IMPORTANT LINEAR ALGEBRA VIDEO - Invertible Matrix Theorem ON ROIDS [Passing Linear Algebra] MOST IMPORTANT LINEAR ALGEBRA VIDEO - Invertible Matrix Theorem ON ROIDS [Passing Linear Algebra]
If A is nxn, then det(cA) = c^ndet(A) If A is nxn, then det(cA) = c^ndet(A)
Invertible iff Det not 0 Invertible iff Det not 0