Matrix

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #11

If `A` & `B` be two symmetric matrices, then the matrix `AB` will be symmetric if - (a) `AB=O` (b) `AB=BA` (c) `|AB|=0` (d) None of these.
Ans: (b) `AB=BA`
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Question No: #12

If `A` & `B` both are symmetric matrices, then the matrix `ABA` is -- (a) symmetric (b) skew-symmetric (c) diagonal (d) none of these
Ans: (a) symmetric
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Question No: #13

If a matrix `A` is both symmetric & skew-symmetric, then `A` should be -- (a) diagonal matrix, (b) zero matrix, (c) square matrix, (d) none of these.
Ans: (b) zero matrix
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Question No: #14

If the matrices `A`, `B` are such that `AB=A` and `BA=B`. Then `B^2` is -- (a) `B`, (b) `A`, (c) `I`, (d) `O`
Ans: (a) `B`
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Question No: #15

If the matrix `A` is proper orthogonal, then value of `|A|` is -- (a) 0, (b) 1, (c) 2, (d) 3
Ans: (b) 1
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Question No: #16

If `\omega` is the imaginary cube root of 1 and $ A = \begin{pmatrix} 1 & 0 \\ 0 & \omega \end{pmatrix} $, $ B = \begin{pmatrix} \omega & 0 \\ 0 & 1 \end{pmatrix} $, then `(A+B)^47` is -- (a) `-I_2`, (b) `\omega\I_2`, (c) `-\omega^2I_2`, (d) `-\omega\I_2`
Ans: (d) `-\omega\I_2`
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Question No: #17

If $ A = \begin{pmatrix} 1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6 \end{pmatrix} $ is a singular matrix, then value of `x` is -- (a) `0`, (b) `1`, (c) `3`, (d) `-3`
Ans: (d) `-3`
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Question No: #18

`A` and `B` are two matrices such that `A\cdotB=O` (where `O` is zero matrix). Can we deduce that either `A` or `B` is a zero matrix? Illustrate by an example.
Ans: `A` or `B` may not be zero matrix
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Question No: #19

`A` is a matrix of order `2\times\m` and `B` is a matrix of order `3\times\n` . If `A\cdot\B` is defined and its order is `p\times\4`, then find the value of `m, n, p`.
Ans: m=3, n=4, p=2
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Question No: #20

For any two square matrices `A` & `B`, when the matrix equation `A^2-B^2 = (A+B)(A-B)` holds true?
Ans: when `AB = BA`
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