Mathematics Tes...

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

Which of the following is not true for the determinant of a square matrix A of order 3?

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

If \(\left| {\;\begin{array}{*{20}{c}} a&b&0\\ 0&a&b\\ b&0&a \end{array}} \right| = 0\) , then which one of the following is correct?

What is the value of the following determinant?

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

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

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 = ?

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 \(\begin{vmatrix} x_1 & y_1 & 1 \\\ x_2 & y_2& 1 \\\ x_3 & y_3 & 1 \end{vmatrix}\) equals:

If A = \(\left[ {\begin{array}{*{20}{c}} {\cos {\rm{\theta }}}&{ - \sin {\rm{\theta }}}\\ {\sin {\rm{\theta }}}&{\cos {\rm{\theta }}} \end{array}} \right]\), then A^-1?

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