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Matrices & Determinants - Past Year Questions

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Q1:

If A=[x1x27y1y2y3z183]A = \begin{bmatrix} x_1 & x_2 & 7 \\ y_1 & y_2 & y_3 \\ z_1 & 8 & 3 \end{bmatrix} is a matrix such that the sum of all three elements along any row, column or diagonal are equal to each other, then the value of determinant of A is:
288
Correct Answer
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Q2:

If A=[123a]A = \begin{bmatrix} 1 & 2 \newline 3 & a \end{bmatrix} where aa is a real number and det (A3−3A2−5A)=0(A ^ 3 - 3A ^ 2 - 5A) = 0 then one of the values of aa can be
Answer options
Option: 2
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Q3:

If A=[10120]A=\left[\begin{array}{ll}1 & 0 \\ \frac{1}{2} & 0\end{array}\right] then A2022A^{2022} is
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Option: 4
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Q4:

Suppose a,ba, b and cc are integers such that a>b>c>0a>b>c>0, and A=[abcbcacab]A=\left[\begin{array}{lll}a & b & c \\ b & c & a \\ c & a & b\end{array}\right]. Then the value of the determinant of AA is
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Option: 3
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Q5:

If A=[100001010]A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0\end{array}\right], then the absolute value of the determinant of (A9+A6+A3+A)\left(A^{9}+A^{6}+A^{3}+A\right) is __________.
32
Correct Answer
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Q6:

If A,BA, B and A+BA + B are non singular matrices and AB=BAAB = BA then 2A−B−A(A+B)−1A+B(A+B)−1B2A - B - A(A + B)^{-1}A + B(A + B)^{-1} B equals
Answer options
Option: 1
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Q7:

A 2×22 \times 2 matrix is filled with four distinct integers randomly chosen from the set {1,2,3,4,5,6}\{1,2,3,4,5,6\}. Then the probability that the matrix generated in such a way is singular is
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Option: 1
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Q8:

Suppose ∣aa2a3−1bb2b3−1cc2c3−1∣=0\left|\begin{array}{lll}a & a^{2} & a^{3}-1 \\ b & b^{2} & b^{3}-1 \\ c & c^{2} & c^{3}-1\end{array}\right|=0, where a,b\mathrm{a}, \mathrm{b} and c\mathrm{c} are distinct real numbers. If a=3{a}=3, then the value of abcabc is:
1
Correct Answer
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Q9:

If inverse of the matrix [2−0.5−1x]\left[\begin{array}{cc}2 & -0.5 \\ -1 & x\end{array}\right] is [1124]\left[\begin{array}{ll}1 & 1 \\ 2 & 4 \end{array}\right], then the value of xx is
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Option: 1
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Q10:

If AA is a 3×33 \times 3 non-zero matrix such that A2=0A^2 = 0 then the determinant of (I+A)50−50A(I + A)^{50} - 50A is equal to
1
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Q11:

Let A,B,CA, B, C be three 4×44 \times 4 matrices such that det A=5,det B=−3det \ A = 5, det \ B = -3, and det C=12det \ C = \frac{1}{2}. Then the detdet 2AB−1C3BT2AB^{-1}C^3B^T is
10
Correct Answer
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Q12:

If a 3×33 \times 3 matrix is filled with +1's and -1's such that the sum of each row and column of the matrix is 1, then the absolute value of its determinant is
4
Correct Answer
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Matrices & Determinants - Past Year Questions (Free PDF Download)

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