List of top Mathematics Questions on Matrices

If \[ A= \begin{bmatrix} c & -a & b\\ a & b & -c\\ -b & c & a \end{bmatrix}, \qquad B= \begin{bmatrix} 1 & 0 & 2\\ 0 & 1 & 2\\ 1 & 2 & 0 \end{bmatrix} \] and \[ AB= \begin{bmatrix} 4 & 4 & -2\\ 1 & 1 & 10\\ -1 & 5 & -4 \end{bmatrix}, \] then \(a^2+b^2+c^2=\)

If \[ A= \begin{bmatrix} 2 & -3 & 1\\ -3 & 1 & -2\\ 1 & -2 & 3 \end{bmatrix}, \] then \(\operatorname{Adj}(A)=\)

If \[ A= \begin{bmatrix} 1&1\\ 0&1 \end{bmatrix} \] and \[ S=A+A^{2}+A^{3}+...+A^{12} \] then sum of all elements of matrix S is

If \[ A= \begin{bmatrix} 0&\alpha&\beta\\ \beta&\alpha&0\\ \alpha&0&\beta \end{bmatrix} \] where \(\beta>\alpha>0\) and \[ AA^T= \begin{bmatrix} 25&a&b\\ a&25&12\\ b&a&25 \end{bmatrix} \] then \[ a+b+\alpha-\beta= \]

For \( I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \), if \( A = \begin{bmatrix} a & b \\ c & -a \end{bmatrix} \) be such that \( A^2 = I \), then :

If \(A = \left[ \begin{array}{ccc}3 & 2 & 6 \\ 1 & 1 & 2 \\ 2 & 2 & 5\end{array} \right]\), \(B = \left[ \begin{array}{c}1 \\ 0 \\ 1\end{array} \right]\) such that \(XA = B^T\) and \(A^{-1}Y = B\), then \(XY =\)

Let \(A = [\begin{array}{cc}a & 1 \\ 1 & b\end{array}]\), where \(a\) and \(b\) are the roots of the equation \(x^2-4x+2 = 0\). If \(A+A^{-1} = kI_2\), then the value of \(k\) is ____

If matrix \(A = \left[ \begin{array}{ccc}-1 & 2025 & 2026 \\ 0 & 2 & 2027 \\ 0 & 0 & -1\end{array} \right]\), then the sum of all elements in \(\text{adj}(A^{-1})\) is equal to...

If \(A = [a_{ij}]_{3\times 3}\), where \(a_{ij} = \{\begin{array}{cc}1, & \text{if }i+j\text{ is even} \\ 0, & \text{if }i+j\text{ is odd}\end{array}\), then \(\text{adj}(A) = \ldots\) ..

Let \(A = [\begin{array}{cc}-3 & 2 \\ 1 & 4\end{array}]\) and if \(A^2-2A+I = [\begin{array}{cc}18 & p \\ q & 11\end{array}]\), then \(\ldots\)

Let \(A = \left[ \begin{array}{ccc}cosα & -sinα & 0 \\ sinα & cosα & 0 \\ 0 & 0 & 1\end{array} \right]\). If \(B = \text{adj}\,A\), then the matrix \(B^{-1}\) is equal to...

Let \(A = [\begin{array}{cc}3 & -4 \\ 1 & -1\end{array}]\) and \(B = [\begin{array}{cc}6 & -13 \\ 5 & -10\end{array}]\) be two matrices. If the variables \(x\) and \(y\) satisfy the matrix equation \(((A^{-1})^2+B)[\begin{array}{c}x \\ y\end{array}] = [\begin{array}{c}0 \\ 0\end{array}]\), then the ordered pair \((x,y) =\)

If \(f(x) = \frac{1-x}{1+x}\), then \(f(f(cosx)) =\)

If the matrix \(A = [\begin{array}{cc}4 & 1 \\ 3 & 2\end{array}]\) is expressed as the sum of a symmetric matrix B and a skew symmetric matrix C then which of the following relations is correct?

If \(A = [\begin{array}{cc}2 & 3 \\ 5 & -2\end{array}]\), \(B^{-1} = \left[ \begin{array}{cc}\frac{1}{5} & \frac{2}{5} \\ \frac{2}{5} & -\frac{1}{5}\end{array} \right]\), then \((AB)^{-1} =\)

If \(A = [\begin{array}{cc}2 & -1 \\ 0 & 2\end{array}]\) and \(A^2+xA+yI_2 = O_2\), where \(I_2\) and \(O_2\) are the identity matrix and null matrix of order 2 respectively, then:

If \(A = [\begin{array}{cc}5a & -b \\ 3 & 2\end{array}]\) and \(A\,(\text{adj }A) = AA^T\), Then \(5a+b =\)

Inverse of \([\begin{array}{cc}3 & -2 \\ 1 & 4\end{array}]\) is

If \(A = [\begin{array}{cc}cosθ & -sinθ \\ sinθ & cosθ\end{array}]\), then the matrix \(A^{-3}\) when \(θ = \frac{π}{6}\) is equal to...

If \(A = [\begin{array}{cc}secθ & -tanθ \\ -tanθ & secθ\end{array}]\), \(θ\in (0,\frac{π}{2})\) such that \(A+adj\,A = 4I\), then \(θ =\)

Let \(A = [\begin{array}{cc}-5 & -3 \\ 2 & 1\end{array}]\). The Row transformation \(R_1\rightarrow R_1+3R_2\) will transform matrix A into

If \(A = \frac{1}{2}[\begin{array}{cc}-1 & -\sqrt{3} \\ \sqrt{3} & -1\end{array}]\) then \(A^{-1}-A^2\) is not

If \(A=\begin{bmatrix}1&2&3\\3&-2&1\\4&2&1\end{bmatrix}\), then show that \(A^3-23A-40I=0\).

If \(A=\begin{bmatrix}2&3\\1&-4\end{bmatrix},\ B=\begin{bmatrix}1&-2\\-1&3\end{bmatrix}\), then find \((AB)^{-1}\).

If \(A^2=A\), then simplify \((I+A)^2 - 7A\), where \(A\) is a square matrix.