Question

Show that a square matrix P over the integers has an inverse with integer entries if...

Show that a square matrix P over the integers has an inverse with integer entries if and only if P is unimodular, that is, the determinant of P is ±1.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Show that if a square matrix K over Zp ( p prime) is involutory ( or...
Show that if a square matrix K over Zp ( p prime) is involutory ( or self-inverse), then det K=+-1 (An nxn matrix K is called involutory if K is invertible and K-1 = K) from Applied algebra show details
please choose your favorite, unique 3x3 Matrix A containing no more than two 0 entries and...
please choose your favorite, unique 3x3 Matrix A containing no more than two 0 entries and having a nonzero determinant. I suggest choosing a matrix with integer elements (e.g. not fractions or irrational numbers) for computational reasons. What is your matrix A? What is det (A)? What is AT? What is det (AT)? Calculate A AT. Show that A AT is symmetrical. Calculate AT A Calculate the determinant of (A AT) and the determinant of (AT A). Should the determinants...
Let A be a square matrix with an inverse A-1. Show that if Ab = 0...
Let A be a square matrix with an inverse A-1. Show that if Ab = 0 then b must be the zero vector.
A stochastic matrix is a square matrix A with entries 0≤a_ij≤1 such that the sum of...
A stochastic matrix is a square matrix A with entries 0≤a_ij≤1 such that the sum of each column of A is 1. Prove that if A is stochastic, then A^k is stochastic for every positive integer k.
A) Find the inverse of the following square matrix. I 5 0 I I 0 10...
A) Find the inverse of the following square matrix. I 5 0 I I 0 10 I (b) Find the inverse of the following square matrix. I 4 9 I I 2 5 I c) Find the determinant of the following square matrix. I 5 0 0 I I 0 10 0 I I 0 0 4 I (d) Is the square matrix in (c) invertible? Why or why not?
(a) Find the inverse of the following square matrix. I 5 0 I I 0 10...
(a) Find the inverse of the following square matrix. I 5 0 I I 0 10 I (b) Find the inverse of the following square matrix. I 4 9 I I 2 5 I (c) Find the determinant of the following square matrix. I 5 0 0 I I 0 10 0 I I 0 0 4 I (d) Is the square matrix in (c) invertible? Why or why not?
Let A be a square matrix, A != I, and suppose there exists a positive integer...
Let A be a square matrix, A != I, and suppose there exists a positive integer m such that Am = I. Calculate det(I + A + A2+ ··· + Am-1).
Show that there is no matrix with real entries A, such that A^2 = [ 0...
Show that there is no matrix with real entries A, such that A^2 = [ 0 1 0 0 ]. (its a 2x2 matrix)
Argue that the only way for a square matrix Ain reduced echelon form Arr to have...
Argue that the only way for a square matrix Ain reduced echelon form Arr to have a non-zero determinant is if Arr=I, the identity matrix.
(1) A square matrix with entries aj,k , j, k = 1, ..., n, is called...
(1) A square matrix with entries aj,k , j, k = 1, ..., n, is called diagonal if aj,k = 0 whenever j is not equal to k. Show that the product of two diagonal n × n-matrices is again diagonal.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT