Final answer:
The question analyzes the properties of matrix A, which is square, symmetric, singular, and diagonal. These terms indicate that A has equal rows and columns, is identical to its transpose, has no inverse, and has all non-diagonal elements as zero. Since it is singular, all diagonal elements must be zero, making A a zero matrix.
Step-by-step explanation:
The question pertains to the properties of a matrix A. Given that matrix A is a square matrix, symmetric, singular, and diagonal, we should understand what each of these terms means:
- Square matrix: A matrix is square if it has the same number of rows and columns.
- Symmetric matrix: A matrix is symmetric if the element at the ith row and jth column is the same as the element at the jth row and ith column, meaning A = AT.
- Singular matrix: A matrix is singular (or noninvertible) if it does not have an inverse, which typically means its determinant is zero.
- Diagonal matrix: A diagonal matrix is a matrix where all off-diagonal entries are zero. Only the diagonal elements (top left to bottom right) may be non-zero.
Since matrix A is also singular, all diagonal elements in this case must be zero because a nonzero determinant would imply that the matrix is invertible. Hence, A is a zero matrix.