# GATE Questions & Answers of Matrix Algebra

## What is the Weightage of Matrix Algebra in GATE Exam?

Total 7 Questions have been asked from Matrix Algebra topic of Linear Algebra subject in previous GATE papers. Average marks 1.71.

For matrices of same dimension M, N and scalar c, which one of these properties DOES NOT ALWAYS hold?

Consider the matrix

${J}_{6}=\left[\begin{array}{cccccc}0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 1& 0& 0& 0& 0& 0\end{array}\right]$

which is obtained by reversing the order of the columns of the identity matrix I6.

Let $P={I}_{6}+\alpha {J}_{6,}$ where $\alpha$ is a non-negative real number. The value of $\alpha$ for which det (P) = 0 is _____

The determinant of matrix A is 5 and the determinant of matrix B is 40. The determinant of matrix AB  is ________.

The maximum value of the determinant among all 2×2 real symmetric matrices with trace 14 is ________.

Let A be an m x n matrix and B an n x m matrix. It is given that determinant (Im + AB) = determinant (In +BA) , where Ik is the k x k identity matrix. Using the above property, the determinant of the matrix given below is

$\left[\begin{array}{cccc}2& 1& 1& 1\\ 1& 2& 1& 1\\ 1& 1& 2& 1\\ 1& 1& 1& 2\end{array}\right]$

$\mathbit{A}=\left[\begin{array}{cc}-5& -3\\ 2& 0\end{array}\right]$ and $\mathbit{I}=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$, the value of A3 is
Consider the matrix $\mathbf{P}=\left[\begin{array}{cc}0& 1\\ -2& -3\end{array}\right]$. The value of ep is