Math: matrices

posted by .

If A and B are both square n x n matrices,

If AB = I,
prove BA = I

Presumably you have to do this without using the usual properties of the inverse of matrices. But we do need to use that if there exists a matrix B such that

A B = I

then the equation A X = 0 has the unique solution:

X = 0

So, let's start with:
AB = I

Multiply both sides by A on the right:

(AB)A = A

Now you use that (AB)A = A(BA) and you can rewrite the above equation as:

A(BA - I) = 0

And it follows that

BA = I

well if u decmial the 7 to a 6 good luck with that ..........

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math (matrices)

    No one answered my matrix question. Let me rephrase: Let A, B, and 0 be 2x2 matrices. Assuming that A is invertible and 0 is all zeroes, what is the inverse of the matrix [A|0] [B|A] (that is a 4x4 matrix represented as 4 2x2 matrices) …
  2. linear algebra

    if: A and B are matrices and A^2 is similar to B^2 Is A guaranteed to be similar to B?
  3. matrices

    Two matrices can be multiplied only if their sizes are compatible. Suppose that U is an m × n matrix, and that V is a p × q matrix. In order for U•V to make sense, what must be true of the dimensions of these matrices?
  4. Math

    I have a few questions about T-Matrix. In excel, I am suppose to work with powered matrices to construct a weighted T matrix, using a scalar of .7. Does this mean I multiply each of the powered matrices by .7?
  5. Linear algebra

    find the inverse of the following matrices if they exist. [1 -2 3] [3 1 0] [-2 1 1] the following represent a 3 x 3 matrices
  6. Urgent please help! matrices

    solve using matrices x+3y-3z=12 3x-y+4z=0 -x+2y-z=1
  7. Matrices (math)

    0.433= (45.6*A) + (3.152*B) 0.3363= (11.92*A) + (37.675*B) Solve for A and B using matrices
  8. math

    Which of the following subsets of the vector space Mnn are subspaces?
  9. maths

    If two matrices are known and are inverse of each other.How can we use these matrices to find the point of intersections for the given set of 3D planes?
  10. Matrices

    Solve the system using matrices. Show all the row operations that you use. 3x-9y=30 2x+5y= -2

More Similar Questions