JEE Main Mathematics: Matrices & Determinants Practice Questions

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

Q1.
$What is the value of the determinant of an identity matrix of order 3?$
Easy
Q2.
$If A is a square matrix such that A squared equals A, then A is called what?$
Easy
Q3.
$If a matrix A has 12 elements, what are the possible orders it can have?$
Easy
Q4.
$If the matrix A = [[0, 5], [5, 0]], find A transpose.$
Easy
Q5.
$Find the value of the determinant of the matrix [[2, 4], [-1, 2]].$
Easy
Q6.
$I f A = [[cos t h e t a, - s in t h e t a], [s in t h e t a, cos t h e t a]], t h e n A^{n} i se q u a l t o :$
Medium
Q7.
$I f A i s a 3 x 3 ma t r i x s u c h t ha t A^{2} = A an d I i s t h e i d e n t i t y ma t r i x, t h e n t h e v a l u eo f (I + A)^{n} i se q u a l t o :$
Medium
Q8.
$If the system of equations x + y + z = 6, x + 2y + 3z = 10, and x + 2y + lambda z = mu has no solution, then:$
Medium
Q9.
$I f A i s a s q u a r e ma t r i x s u c h t ha t A^{T} A = I, t h e n t h e d e t er minan t o f A i s :$
Medium
Q10.
$T h e v a l u eo f t h e d e t er minan t o f t h e ma t r i x [[1, a, a^{2}], [1, b, b^{2}], [1, c, c^{2}]] i s :$
Medium
Q11.
$L e t A b e a 3 x 3 ma t r i x s u c h t ha t A^{T} A = I an dd e t (A) = 1. T h e n d e t (A - I) i se q u a l t o :$
Hard
Q12.
$L e t A b e a 3 x 3 ma t r i x s u c h t ha t A^{2} = I an d A i s n o t e q u a l t o I or - I . I f t h e t r a ceo f A i s 1, f in d t h e d e t er minan t o f A .$
Hard
Q13.
$If the system of equations x + y + z = 6, x + 2y + 3z = 10, and x + 2y + kz = m has no solution, then:$
Hard
Q14.
$I f A i s a s k e w - sy mm e t r i c ma t r i x o f or d er 3, t h e n t h e v a l u eo f t h e d e t er minan t o f A^{4} i s a l w a y se q u a l t o :$
Hard

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