If A = [[2, 3], [1, 4]], find A⁻¹.

If A is a 3 × 3 matrix with A² = A and A is not the identity, what is such a matrix called?

If A = [[1, 2], [3, 4]] and B = [[0, 1], [1, 0]], find AB and BA and state whether they are equal.

Define a symmetric and a skew-symmetric matrix, and state what can be said about the diagonal of a skew-symmetric matrix.

Prove that (AB)^T = B^TA^T for matrices for which the product is defined.

Evaluate the integral of x² with respect to x, and the definite integral of x² from 0 to 1.

Find the principal value of sin⁻¹(−1/2) and cos⁻¹(−1/2).