Matrices

If B is an m × n matrix, then it has mn elements.

• True

• False

If B is an m × n matrix, then B has m columns.

• True

• False

Matrices can be added only if they have the same dimensions.

• True

• False

If A and B are both n × n matrices, then AB = BA.

• True

• False

For all n × n matrices A, B, and C, A(B + C) = (B + C)A.

• True

• False

If all the entries of a matrix are positive, the determinant must be positive.

• True

• False

The following matrix has an inverse.

• True

• False

Matrix A cannot have an inverse if |A| = 0.

• True

• False

For A to have an inverse, A must be a square matrix.

• True

• False

If A is the inverse of B, then B is the inverse of A.

• True

• False