List of top Mathematics Questions on Matrices and Determinants asked in JEE Main

If the following system of linear equations
\( 2x + y + z = 5 \)
\( x - y + z = 3 \)
\( x + y + az = b \)
has no solution, then :
If for the matrix, A = \( A = \begin{bmatrix} 1 & -\alpha \\ \alpha & \beta \end{bmatrix} \), and \( A A^T = I_2 \), then the value of \( \alpha^4 + \beta^4 \) is :
Let A be a 3$\times$3 matrix with det(A)=4. Let R$_i$ denote the i$^{th}$ row of A. If a matrix B is obtained by performing the operation R$_2$ $\rightarrow$ 2R$_2$+5R$_3$ on 2A, then det(B) is equal to:
The following system of linear equations
2x + 3y + 2z = 9
3x + 2y + 2z = 9
x - y + 4z = 8
For real numbers $\alpha$ and $\beta$, consider the following system of linear equations:
$x+y-z=2$
$x+2y+\alpha z = 1$
$2x-y+z = \beta$
If the system has infinite solutions, then $\alpha+\beta$ is equal to _________.
Let \( A = \begin{bmatrix} x & y & z \\ y & z & x \\ z & x & y \end{bmatrix} \), where \( x, y \) and \( z \) are real numbers such that \( x + y + z > 0 \) and \( xyz = 2 \). If \( A^2 = I_3 \), then the value of \( x^3 + y^3 + z^3 \) is __________.
If \( A = \begin{pmatrix} 1 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{pmatrix} \) and \( M = A + A^2 + A^3 + \cdots + A^{20} \), then the sum of all the elements of the matrix \( M \) is equal to ________.
Let A and B be 3 × 3 real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear equations (A²B² - B²A²) X = O, where X is a 3 × 1 column matrix of unknown variables and O is a 3 × 1 null matrix, has :