(A^T)^-1 = (A^-1)^T  

(A^T)^-1 = (A^-1)^T  

(AB)^-1 =

B^-1A^-1

If det(A) = 0 then...

Matrix is singular

if det(A)≠0 then...

A is invertible or

non-singular

If A is invertible,

det(A^-1) =

If A is invertible,

det(A^-1) =      1

                            det(A)

det(A) = (transpose)

det(A) = det(A^T)

(n×n matrix)

det(cA) = cⁿ det(A)

det(cA) = cⁿ det(A)

(A)(A^-1)=

(A)(A^-1)=I

(A^-1)^-1=

(A^-1)^-1=A

(A^k)^-1=

(A^k)^-1= (A^-1)^k

(cA)^-1 = 1/c (A^-1)

(cA)^-1 = 1/c (A^-1)

A(BC) =

(AB)C

A(B+C) =

A(B+C) = AB+AC

(A+B)C =

(A+B)C = AC+BC

c(AB) = (cA)B = A(cB)

c(AB) = (cA)B = A(cB)

Stochaistic

↓ 

x  x  x  x    →

x  x  x  x    →

x  x  x  x    →

Stochaistic

FROM

↓ 

x  x  x  x    →

      x  x  x  x    →  TO

x  x  x  x    →

true or false:

Matrix Addition is commutative

true.

A+B = B+A

true or false:

The inverse of a non-singular matrix is unique.

True.

true or false:

If the matrices A,B and C satisfy

BA=CA and a is invertible, then B=C

True

 true or false

(AB)^-1 = A^-1B^-1

False,

(AB)^-1 = B^-1A^-1

true of false:

If A can be reduced to the identity matrix, the A is non-singular.

true.

if

A is m×n and B is n×p

how big is the resulting matrix?

m×p

if

A is 4×1 and B is 1×3

how big is the resulting matrix?

4×3

if

A is 1×4 and B is 3×1

how big is the resulting matrix?

The product isn't defined.

You can't do that.

Interchanging two rows of a matrix

changes the sign of it's determinant.

True

Multiplying a row of a matrix by a non-zero constant results in the determinant of the matrix being multiplied by the same constant.

True

True