List of top Mathematics Questions on Matrices asked in JEE Main

Let I be an identity matrix of order 2 × 2 and P = [2 -1; 5 -3]. Then the value of n ∈ N for which Pⁿ = 5I - 8P is equal to ________.

Let \(S = \left\{ n \in \mathbb{N} : \begin{pmatrix} 0 & i \\ 1 & 0 \end{pmatrix}^n \begin{pmatrix} a & b \\ c & d \end{pmatrix} = \begin{pmatrix} a & b \\ c & d \end{pmatrix}, \forall a, b, c, d \in \mathbb{R} \right\}\), where \(i = \sqrt{-1}\). Then the number of 2-digit numbers in the set S is __________.

If for a matrix A, |A| = 6 and adj $A = \begin{bmatrix}1&-2&4\\ 4&1&1\\ -1&k&0\end{bmatrix}$ , then k is equal to :

If A = $ \begin {bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b \end {bmatrix}$ is a matrix satisfying the equation $AA^T =9 I,$ where, $I$ is $3 \times 3$ identity matrix, then the ordered pair $(a, b)$ is equal to

If $ X+Y=\left[ \begin{matrix} 7 & 0 \\ 2 & 5 \\ \end{matrix} \right] $ and $ X-Y=\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \\ \end{matrix} \right] $ , then X is equal to

The rank of $\left[\begin{array}{lll}4& 0& 0\\ 0& 3& 0\\ 0& 0& 5\end{array}\right]$ is equal to

A=\(\begin{bmatrix}   2 & -1 \\   1 & 1  \end{bmatrix}\)if sum of diagonal elements of A¹³ is 3ⁿ then n equal to: