Question

If \[A=[a_{ij}]_{m \times n}\] and \[B=[b_{ij}]_{m \times n}\], which statement expresses \[A=B\]?

Options

• \[A=B \iff m\ne n\]

• \[A=B \iff a_{ij}=b_{ij}\text{ for all }i,j\]

• \[A=B \iff a_{ij}\ne b_{ij}\text{ for all }i,j\]

• \[A=B \iff a_{ij}=b_{ji}\text{ for all }i,j\]

Answer 1

For matrices of order \[m\times n\], equality requires \[a_{ij}=b_{ij}\] for all \[i,j\]. Each element must equal the element in the same position.