JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A\) and \(B\) be two invertible matrices of order \(3 \times 3\). If det \((ABA^T) = 8\) and \(det\,(AB^{-1}) = 8\), then \(det\, (BA^{-1} B^T)\) is equal to
- A \(\frac{1}{4}\)
- B \(1\)
- C \(\frac{1}{16}\)
- D \(16\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{16}\)
Step-by-step Solution
Detailed explanation
\(\left| {AB{A^T}} \right| = \left| A \right|.\left| B \right|.\left| {{A^T}} \right| = {\left| A \right|^2}\left| B \right|\) \(\left| {A{B^{ - 1}}} \right| = 8 \Rightarrow \left| A \right| = 8\left| B \right|\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let \(\mathrm{A}=\{1,2,3,4\}\) and \(\mathrm{B}=\{1,4,9,16\}\). Then the number of many-one functions \(f: \mathrm{A} \rightarrow \mathrm{B}\) such that \(1 \in f(\mathrm{~A})\) is equal to :JEE Mains 2025 Hard
- \(\frac{2^{3}-1^{3}}{1 \times 7}+\frac{4^{3}-3^{3}+2^{3}-1^{3}}{2 \times 11}+\)\(\frac{6^{3}-5^{3}+4^{3}-3^{3}+2^{3}-1^{3}}{3 \times 15}+\ldots .+\) \(\frac{30^{3}-29^{3}+28^{3}-27^{3}+\ldots+2^{3}-1^{3}}{15 \times 63}\)is equal to.JEE Mains 2022 Hard
- Let \(y=y(x)\) be the solution of the differential equation \(2 \cos x \frac{\mathrm{~d} y}{\mathrm{~d} x}=\sin 2 x-4 y \sin x, x \in\left(0, \frac{\pi}{2}\right)\). If \(y\left(\frac{\pi}{3}\right)=0\), then \(y^{\prime}\left(\frac{\pi}{4}\right)+y\left(\frac{\pi}{4}\right)\) is equal to ________.JEE Mains 2025 Easy
- Let \(f\left( x \right) = \int\limits_0^x {g\left( t \right)dt} \), where \(g\) is a non zero even function. If \(f(x+5) = g(x)\) , then \(\int\limits_0^x {f\left( t \right)dt} \) equalsJEE Mains 2019 Hard
- The area of the region bounded by the curve \(y=\max \{|x|, x|x-2|\}\), then \(x\)-axis and the lines \(x=-2\) and \(x=4\) is equal to _______ .JEE Mains 2025 Easy
- Let the vectors \((2+a+b) \hat{i}+(a+2 b+c) \hat{j}-(b+c) \hat{k}\) \((1+\mathrm{b}) \hat{i}+2 \mathrm{b} \hat{j}-\mathrm{b} \hat{k}\) and \((2+\mathrm{b}) \hat{i}+2 \mathrm{b} \hat{j}+(1-\mathrm{b}) \hat{k}\) \(\mathrm{a}, \mathrm{b}, \mathrm{c} \in \mathrm{R}\) be co-planar. Then which of the following is true?JEE Mains 2021 Hard
More PYQs from JEE Mains
- The line \(y=x+1\) meets the ellipse \(\frac{x^{2}}{4}+\frac{y^{2}}{2}=1\) at two points \(P\) and \(Q\). If \(r\) is the radius of the circle with \(PQ\) as diameter then \((3 r )^{2}\) is equal toJEE Mains 2022 Hard
- Let the foci and length of the latus rectum of an ellipse \(\frac{\mathrm{x}^2}{\mathrm{a}^2}+\frac{\mathrm{y}^2}{\mathrm{~b}^2}=1, \mathrm{a}>\mathrm{b}\) be \(( \pm 5,0)\) and \(\sqrt{50}\), respectively. Then, the square of the eccentricity of the hyperbola \(\frac{\mathrm{x}^2}{\mathrm{~b}^2}-\frac{\mathrm{y}^2}{\mathrm{a}^2 \mathrm{~b}^2}=1\) equalsJEE Mains 2024 Hard
- The sum of squares of all possible values of \(k\), for which area of the region bounded by the parabolas \(2 \mathrm{y}^2=\mathrm{kx}\) and \(\mathrm{ky}^2=2(\mathrm{y}-\mathrm{x})\) is maximum, is equal to :JEE Mains 2024 Hard
- A ray of light passing through the point \(P (2,3)\) reflects on the \(x-\)axis at point \(A\) and the reflected ray passes through the point \(Q(5,4)\). Let \(R\) be the point that divides the line segment \(AQ\) internally into the ratio \(2: 1\). Let the co-ordinates of the foot of the perpendicular \(M\) from \(R\) on the bisector of the angle \(PAQ\) be \((\alpha, \beta)\). Then, the value of \(7 \alpha+3 \beta\) is equal to.......JEE Mains 2022 Hard
- Let the numbers \(2, b, c\) be in an \(A.P\) and \(A = \left[ {\begin{array}{*{20}{c}}
1&1&1 \\
2&b&c \\
4&{{b^2}}&{{c^2}}
\end{array}} \right]\). If \(det(A) \in [2,16]\) then \(c\) lies in the intervalJEE Mains 2019 Hard - Tangent and normal are drawn at \(P(16, 16)\) on the parabola \({y^2} = 16x\), which intersect the axis of the parabola at \(A\) and \(B\), respectively. If \(C\) is the centre of the circle through the points \(P, A\) and \(B\) and \(\angle CPB = \theta \) , then a value of \(\tan \theta \;\)is :JEE Mains 2018 Hard