AP EAMCET · Maths · Matrices
Let \(M\) and \(N\) be two invertible square matrices over \(R\) of order 2 such that \(N\) is diagonal. Then \(M N M^{-1}\) is diagonal ____
- A For all \(M\)
- B Only when \(M\) is a scalar matrix
- C For all diagonal matrices \(M\)
- D \(M\) must be a null matrix
Answer & Solution
Correct Answer
(C) For all diagonal matrices \(M\)
Step-by-step Solution
Detailed explanation
Let the real matrices of order 2 \(M=\left[\begin{array}{ll} a & b \\ c & d \end{array}\right] \text { and } N=\left[\begin{array}{cc} n_1 & 0 \\ 0 & n_2 \end{array}\right]\) \(\because M\) and \(N\) are invertible matrices, so…
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
- If \(I\) is the incentre of \(\triangle A B C\) and \(P_1, P_2, P_3\) are respectively the radii of the circumcircles of the \(\triangle I B C, \triangle I C A\) and \(\triangle I A B\), then \(P_1 P_2 P_3=\)AP EAMCET 2018 Hard
- The mean deviation from the mean for the data \(6,7,10\), \(12,13,4,12,16\) isAP EAMCET 2023 Easy
- Suppose a circle passes through \((0, a)\) and \((b, h)\) having its centre at \((c, 0)\). Then the value of \(c\) isAP EAMCET 2022 Medium
- The number of words which can be made out of the letters of the word 'MOBILE' when consonants occupy odd places isAP EAMCET 2021 Easy
- If thenAP EAMCET 2018 Medium
- A line passing through the point \(P(1,1)\) and parallel to the line \(x-y=5\) cuts the line \(x+3 y-2=0\) at \(Q\). Then twice the length of the segment \(P Q\) isAP EAMCET 2017 Medium
More PYQs from AP EAMCET
- The shapes of \(\mathrm{XeF}_2, \mathrm{XeF}_4\), and \(\mathrm{XeO}_3\) respectively areAP EAMCET 2022 Medium
- \(\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}\) are electromagnetic radiations. Frequencies of \(\mathrm{a}, \mathrm{b}\) are \(3 \times 10^{15} \mathrm{~Hz}\), \(2 \times 10^{14} \mathrm{~Hz}\), respectively, whereas wavelength of c, d are \(400 \mathrm{~nm}, 750 \mathrm{~nm}\), respectively. The increasing order of their energies isAP EAMCET 2025 Medium
- A PN junction diode is used asAP EAMCET 2024 Easy
- Which of the following is not an air pollutant?AP EAMCET 2005 Easy
- Two boys conducted experiments on the projectile motion with stopwatch and noted some readings. As one boy throws a stone in air at the same angle with the horizontal, the other boy observes that after \(4 \mathrm{~s}\), the stone is moving at an angle \(30^{\circ}\) to the horizontal and after another \(2 \mathrm{~s}\) it is travelling horizontally. The magnitude of the initial velocity of the stone is (Acceleration due to gravity, \(g=10 \mathrm{~ms}^{-2}\).)AP EAMCET 2019 Hard
- Let \(A=\left[\begin{array}{ccc}b^2+c^2 & a^2 & a^2 \\ b^2 & c^2+a^2 & b^2 \\ c^2 & c^2 & a^2+b^2\end{array}\right]\). If
\(a=\sin \frac{\pi}{6}, b=\cos \frac{\pi}{4}\) and \(c=\cot \frac{\pi}{2}\), then \(A\) isAP EAMCET 2022 Easy