matrices

Question 1

when does the inverse of a matrix exist?

Answer 1

if detA is not 0

Question 2

what is the inverse of a 2x2 matrix
a b
c d

Answer 2

1/det * d -b
-c a

Question 3

describe the steps to calculate the inverse of a 3x3 (or larger) matrix

Answer 3

1. find matrix of cofactors (including signs)
2. transpose matrix of cofactors (adjugate matrix)
3. divide adjugate matrix by determinant

Question 4

what is true if two matrices are similar

Answer 4

there exists some invertible matrix M such that
B = M^-1 A M