If A=[ array ll 1 & 2 1 & 1 array ] and B=[ array cc 0 & -1 1 & 2 array ] , then what is B^ -1 A^ -1 equal to?

Correct answer: B. [ array cc -1 & 3 1 & -2 array ] aligned |A| & =-1,| B|=1 A^ -1 & = 1 | A| Adj A=(1)/(-1)[ array cc 1 & -1 -2 & 1 array ]^ T & =[ array cc -1 & 2 1 & -1 array ] aligned aligned & B^ -1 = 1 | B| Adj=(1)/(1)[ array cc 2 & -1 1 & 0 array ]^ T =[ array cc 2 & 1 -1 & 0 array ] & B^ -1 A^ -1 =[ array cc 2 & 1 -1 & 0 array ][ array cc -1 & 2 1 & -1 array ]=[ array cc -1 & 3 1 & -2 array ]. aligned

NDA 2012

Exam: NDA
Year: 2012
Subject: Mathematics
Chapter: Matrices

NDA 2012 · Mathematics · Matrices

If A=[ array ll 1 & 2 1 & 1 array ] and B=[ array cc 0 & -1 1 & 2...

A=\left[

\begin{array}{ll}1 & 2 \\ 1 & 1\end{array}

\right] and

B=\left[

\begin{array}{cc}0 & -1 \\ 1 & 2\end{array}

\right]

, then what is

B^{-1}\mathrm{A}^{-1}$ equal to?

Options

A $\left[$ $\begin{array}{cc}1 & -3 \\ -1 & 2\end{array}$ $\right]$
B $\left[$ $\begin{array}{cc}-1 & 3 \\ 1 & -2\end{array}$ $\right]$
C $\left[$ $\begin{array}{cc}-1 & 3 \\ -1 & -2\end{array}$ $\right]$
D $\left[$ $\begin{array}{cc}-1 & -3 \\ 1 & -2\end{array}$ $\right]$

Correct answer

B. $\left[$ $\begin{array}{cc}-1 & 3 \\ 1 & -2\end{array}$ $\right]$

Step-by-step solution

\begin{aligned} |\mathrm{A}| & =-1,|\mathrm{ B}|=1 \\ \mathrm{ A}^{-1} & =\frac{1}{|\mathrm{ A}|} \operatorname{Adj} \mathrm{A}=\frac{1}{-1}\left[\begin{array}{cc} 1 & -1 \\ -2 & 1 \end{array}\right]^{\mathrm{T}} \\ & =\left[\begin{array}{cc} -1 & 2 \\ 1 & -1 \end{array}\right] \end{aligned}

\begin{aligned} & \mathrm{B}^{-1}=\frac{1}{|\mathrm{ B}|} \mathrm{Adj}=\frac{1}{1}\left[\begin{array}{cc} 2 & -1 \\ 1 & 0 \end{array}\right]^{\mathrm{T}}=\left[\begin{array}{cc} 2 & 1 \\ -1 & 0 \end{array}\right] \\ & \mathrm{B}^{-1} \mathrm{ A}^{-1}=\left[\begin{array}{cc} 2 & 1 \\ -1 & 0 \end{array}\right]\left[\begin{array}{cc} -1 & 2 \\ 1 & -1 \end{array}\right]=\left[\begin{array}{cc} -1 & 3 \\ 1 & -2 \end{array}\right]. \end{aligned}

Practice Matrices on Quantrex Academy →

More from Matrices

Consider the following statements : I. If n× n(n > 1) matrix is symmetric, then its… NDA 2026 If M is a square matrix such that M^3=M , then how many values of |M| are possible ? NDA 2026 If M_k= bmatrix k & k-1 k-1 & k bmatrix where k is a natural number, then what is… NDA 2026 If M^ T is the transpose of a 2×2 matrix M , then which of the following is/are correct ?… NDA 2026 Consider the following in respect of non-singular matrices A and B : I. (AB)^ -1 = A^ -1… NDA 2025 For the following two (02) items: Let A = pmatrix θ & θ - θ & θ pmatrix . What is [adj\… NDA 2025 Consider the following statements about the matrix M = pmatrix 71 & 23 & 48 57 & 28 & 29… NDA 2025 If [x \ 1 \ 1] pmatrix 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 pmatrix pmatrix 1 1 x pmatrix = [45]… NDA 2025 If A = pmatrix 1 & 2 & 2 2 & 1 & 2 2 & 2 & 1 pmatrix , then what is A^2 - 4A equal to? NDA 2025 If A = pmatrix y & z & x z & x & y x & y & z pmatrix where x , y , z are integers, is an… NDA 2025 If A = pmatrix x & y & z y & z & x z & x & y pmatrix where x , y , z are integers, is an… NDA 2025 For the following two (02) items: Let A = pmatrix θ & θ - θ & θ pmatrix . What is the… NDA 2025 What is the value of the determinant of the inverse of the matrix pmatrix -4 & -5 2 & 2… NDA 2025 If f(θ) = pmatrix θ & θ - θ & θ pmatrix , then what is \ f(π)\ ^2 equal to? NDA 2025 Let X be a matrix of order 3 × 3, Y be a matrix of order 2 × 3 and Z be a matrix of order… NDA 2024 Let A and B be two square matrices of same order. If A B is a null matrix, then which one… NDA 2024 Full Matrices list Matrices JEE Maths PYQs JEE Mathematics PYQs All NDA PYQs