Matrices

If A is a 2×3 matrix and B is a 3×2 matrix, what is the order of the matrix product AB?

If A = \(\begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}\), what is det(2A)?

Which of the following matrices is invertible?

If A and B are square matrices of the same order and AB = BA, then which of the following is always true?

Find the inverse of matrix \(\begin{bmatrix}4 & 7 \\ 2 & 6\end{bmatrix}\).

If A is a 3×3 matrix such that A^3 = I (identity matrix), then the matrix A is:

Let A = \(\begin{bmatrix}1 & 2 & 3 \\ 0 & 1 & 4 \\ 5 & 6 & 0\end{bmatrix}\). What is the determinant of A?

If A is a 2×2 matrix with eigenvalues 3 and 5, what is det(2A)?

If A and B are 2×2 matrices such that AB = O (zero matrix) but neither A nor B is zero, then which of the following is true?

Find the rank of matrix \(\begin{bmatrix}1 & 2 & 3 \\ 2 & 4 & 6 \\ 1 & 0 & 1\end{bmatrix}\).