JEE Advanced Mathematics: Matrices & Determinants Practice Questions

10 questions with answers and step-by-step solutions. Tap any question to see the full worked solution.

Q1.
$If A is a square matrix of order 3 such that the determinant of A is 5, then what is the value of the determinant of 3A?$
Easy
Q2.
$If A is a matrix such that A squared equals the identity matrix, then what is the inverse of A?$
Easy
Q3.
$What is the value of the determinant of a skew-symmetric matrix of order 3?$
Easy
Q4.
$If A and B are symmetric matrices of the same order, then which of the following is always true?$
Easy
Q5.
$If the matrix A is given by [[1, 2], [3, 4]], what is the trace of A?$
Easy
Q6.
$If A is a skew-symmetric matrix of odd order, then det(A) is equal to:$
Hard
Q7.
$L e tM b e a 3 x 3 ma t r i x w i t h r e a l e n t r i ess u c h t ha t M^{T} M = I an dd e t (M) = 1. I f M i s n o tt h e i d e n t i t y ma t r i x, f in d t h e v a l u eo f d e t (M - I) .$
Hard
Q8.
$L e t A b e a 3 x 3 ma t r i x s u c h t ha t A^{2} = A an dd e t (A + I) = 4. F in d t h e v a l u eo f d e t (A) .$
Hard
Q9.
$L e t A b e a 3 x 3 ma t r i x s u c h t ha t A^{3} = 0. W hi c h o f t h e f o l l o w in g i s a l w a y s t r u e ?$
Hard
Q10.
$L e t A b e a 2 x 2 ma t r i x s u c h t ha t A^{2} + I = 0. I f A ha sr e a l e n t r i es, f in d t h e t r a ceo f A .$
Hard

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