Determinants & ...

If A and B are two n x n non singular matrix, then _____________

A is a scalar matrix with scalar k ≠ 0 of order 3. Then A^-1 is

What is the value of the following determinant?

\(\begin{vmatrix} cos C & tan A & 0\\ sin B & 0 & -tanA\\ 0 & sinB & cos C \end{vmatrix}\)

Let det M denotes the determinant of the matrix M. Let A and B be 3 × 3 matrices with det  A = 3 and det B = 4. Then the det (2AB) is

An equilateral triangle has each side equal to a. If the co-ordinates of its vertices are (x₁, y₁); (x₂, y₂): (x₃, y₃) then the square of the determinant \(\begin{vmatrix} x_1 & y_1 & 1 \\\ x_2 & y_2& 1 \\\ x_2 & y_2 & 1 \end{vmatrix}\) equals:

If A is a 2 × 2 matrix and |A| = 5, what is |5A| ? (| | denotes determinant)

If \(\Delta=\rm \begin{vmatrix}a_1&b_1&c_1\\\ a_2 &b_2&c_2\\\ a_3&b_3&c_3\end{vmatrix}\) and A₁, B₁, C₁ denote the cofactors of a₁, b₁, c₁ respectively, then the value of the determinant \(\rm \begin{vmatrix}A_1&B_1&C_1\\\ A_2 &B_2&C_2\\ A_3&B_3&C_3\end{vmatrix}\) is

If a₁, a₂, a₃, ..., a₉ are in G.P., then what is the value of the determinant \(\begin{vmatrix} \rm \ln a_1 & \rm \ln a_2 & \rm \ln a_3 \\ \rm \ln a_4 & \rm \ln a_5 & \rm \ln a_6 \\ \rm \ln a_7 & \rm \ln a_8 & \rm \ln a_9 \end{vmatrix}\)?

If \(\left| {\;\begin{array}{*{20}{c}} {x + 2}&2&2\\ 2&{x + 2}&2\\ 2&2&{x + 2} \end{array}} \right|\) = 0, then values of x satisfying this equation are

If \(A = \frac {1}{3} \left( {\begin{array}{*{20}{c}} 1&{2}&2\\ 2&{1}&{-2}\\ -2&2&{-1} \end{array}} \right)\) then (AA^T)^-1 = ?