List of top Mathematics Questions on Matrices asked in MHT CET

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

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:

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

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

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 $A = \begin{bmatrix} 5a & -b \\ 3 & 2 \end{bmatrix}$ and $A \cdot \text{adj } A = A A^T$, then $5a + b = \dots$

Matrix A is non-singular matrix and $(A - 3I)(A - 5I) = 0$, then $\frac{15}{8} A^{-1} = \dots\dots$

If \(A = \left[ \begin{array}{cc} 1 & \cot \frac{\theta}{2} \\ -\cot \frac{\theta}{2} & 1 \end{array} \right]\) then \(A^{-1} =\)

Let \( A \) be a non-singular matrix of order n and \( |A| = k \), then \( (\text{adj} \, A)^{-1} \) is:

The angle between the line \( x = \frac{y-1}{2} = \frac{z-3}{\lambda} \) and the plane \( x + 2y + 3z = 6 \) is \( \cos^{-1} \sqrt{\frac{5}{14}} \), then the value of \( \lambda \) is

Let \( \bar{a}, \bar{b}, \bar{c} \) be three vectors such that \( \bar{a} + \bar{b} + \bar{c} = \bar{0}, |\bar{a}| = 3, |\bar{b}| = 4, |\bar{c}| = 5 \), then \( \bar{a} \cdot \bar{b} + \bar{b} \cdot \bar{c} + \bar{c} \cdot \bar{a} = \)}

If \( (\cos^{-1} x)^2 - (\sin^{-1} x)^2>0 \), then}

If \( \tan \text{A} = \frac{1}{\sqrt{x(x^2+x+1) \), \( \tan \text{B} = \frac{\sqrt{x}}{\sqrt{x^2+x+1}} \) and \( \tan \text{C} = \sqrt{x^{-1} + x^{-2} + x^{-3}} \) then}