Let A = [begin array ccc 0 & 2 & -3 \\-2 & 0 & 1 \\3 & -1 & 0end array ] and B be a matrix such that B ( I - A )= I + A . Then the sum of the diagonal elements of B T B is equal to \ \ \ \ .

Mathematics · Matrices

JEE Main 2026 — 23 January, Evening Shift — Question 24

Let $\mathrm{A}=\left[\begin{array}{ccc}0 & 2 & -3 \\-2 & 0 & 1 \\3 & -1 & 0\end{array}\right]$ and B be a matrix such that $\mathrm{B}(\mathrm{I}-\mathrm{A})=\mathrm{I}+\mathrm{A}$ . Then the sum of the diagonal elements of $\mathrm{B}^{\mathrm{T}} \mathrm{B}$ is equal to $\_\_\_\_$ .

Answer: 3

Numerical answer — enter this value.

Step-by-step solution

$A^{T}=-A$

$\mathrm{B}=(\mathrm{I}+\mathrm{A})(\mathrm{I}-\mathrm{A})^{-1}$

$B^{T}=\left((I-A)^{-1}\right)^{T}(I+A)^{T}$

$B^{T}=\left(I-A^{T}\right)^{-1}\left(I+A^{T}\right)$

$\mathrm{B}^{\mathrm{T}}=(\mathrm{I}+\mathrm{A})^{-1}(\mathrm{I}+\mathrm{A})$

$\mathrm{B}^{\mathrm{T}} \mathrm{B}=(\mathrm{I}+\mathrm{A})^{-1}(\mathrm{I}-\mathrm{A})(\mathrm{I}+\mathrm{A})(\mathrm{I}-\mathrm{A})^{-1}$

$=(\mathrm{I}+\mathrm{A})^{-1}(\mathrm{I}+\mathrm{A})(\mathrm{I}-\mathrm{A})(\mathrm{I}-\mathrm{A})^{-1}$ $=\mathrm{I}$

$\operatorname{tr}\left(\mathrm{B}^{\mathrm{T}} \mathrm{B}\right)=3$

Answer key and solution verified before publishing.

Practise Matrices

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free

Exam: JEE Main 2026
Paper: 23 January, Evening Shift
Subject: Mathematics
Chapter: Matrices
Topic: Inverse of a Matrix

The system of linear equations x+y+z=6 , 2 x+5 y+a z=36 , x+2 y+3 z=b has

Answer: 3

Step-by-step solution

Practise Matrices

More Matrices questions from this paper