The order of the product of two matrices is determined by the outer dimensions. Here, A (2x2) and B (2x3) can be multiplied, resulting in a matrix of order 2x3.

The order of the sum of two matrices is the same as the order of the individual matrices. Therefore, A + B is a 3x3 matrix.

The sum of two matrices is defined only when they have the same order. Since both A and B are 3x3 matrices, A + B will also be a 3x3 matrix.

A 3x3 matrix has 3 rows and 3 columns, resulting in a total of 3 * 3 = 9 elements.

A 3x3 matrix can have a maximum of 3 linearly independent rows, but the answer options are incorrect. The correct answer is 3.

In a diagonal matrix, all non-diagonal elements are zero.

A symmetric matrix satisfies the condition Aij = Aji for all i and j.

The determinant of a 1x1 matrix is simply the value of the single element. Therefore, the determinant of [[5]] is 5.

The determinant of a 2x2 matrix is calculated as ad - bc.

The determinant of a 2x2 matrix is calculated as ad - bc.

The order of a matrix is given by the number of rows followed by the number of columns. Therefore, a matrix with 3 rows and 4 columns is of order 3x4.

The trace of a matrix is the sum of its diagonal elements. For matrix A, the trace is a + d.

The trace of a square matrix is defined as the sum of the elements on its main diagonal.

An identity matrix is defined as a square matrix with all diagonal elements equal to 1 and all other elements equal to 0.

A matrix where all elements are zero is called a zero matrix.

A scalar matrix is a square matrix in which all the elements are equal to the same scalar value.

A skew-symmetric matrix is defined by the property A = -A.

A singular matrix is one that does not have an inverse, which occurs when its determinant is zero. The matrix [[2, 3], [4, 6]] is singular.

A square matrix is one where the number of rows is equal to the number of columns. Among the options, only 3x3 has equal rows and columns.

An identity matrix is a square matrix with ones on the diagonal and zeros elsewhere. The matrix [[1, 0], [0, 1]] fits this definition.

A zero matrix is one where all elements are zero. The matrix [[0, 0], [0, 0]] meets this criterion.

A matrix is not invertible if its determinant is zero. The matrix [[0, 1], [0, 0]] has a determinant of 0.

A symmetric matrix is one that is equal to its transpose. Matrix B is symmetric because B = B^T.