If \(\det(A)\) = 5 for a \(3\times 3\) matrix A, what is \(\det()\)?

If \(\det(A)\) = -2 and \(\det(B)\) = 7 for square matrices of the same size, find \(\det(\(AB\))\).

If A is \(4\times 4\) and \(\det(A)\) = 3, find \(\det(2A)\).

If a matrix has two equal rows, what is its determinant?

A row operation swaps two rows of A to produce B. If \(\det(A)\) = 9, find \(\det(B)\).

A row operation multiplies one row of A by 4 to produce B. If \(\det(A)\) = -3, find \(\det(B)\).

A row operation replaces \(\mathbb R^2\) by \(\mathbb R^2\) + 5R1. How does the determinant change?

If \(\det(A)\) = 6 and A is invertible, find \(\det()\).

If A is a \(3\times 3\) matrix with \(\det(A)\) = 4, find \(\det(-A)\).

A learner claims \(\det(A + B)\) = \(\det(A)\) + \(\det(B)\). Disprove this using \(A=I_2\) and \(B=I_2\).