Inverse of a Matrix
Trending Questions
Q.
If , then is equal to:
None of these
Q. If A and B are square matrices of the same order and A is non-singular, then for a positive integer n, (A−1BA)n is always equal to
Q. If B=⎡⎢⎣52α1021α3−1⎤⎥⎦ is the inverse of a 3×3 matrix A, then the sum of all values of α for which det(A)+I=0, is
- 2
- 1
- 0
- −1
Q. Let A, B, C, D be (not necessarily square) four matrices such that AT=BCD; BT=CDA; CT=DAB and DT=ABC. If S=ABCD, then
- S=S3
- S=S4
- S=S2
- S=S6
Q. If A(α, β)=⎡⎢⎣cos αsin α0−sinαcosα000eβ⎤⎥⎦, then A(α, β)−1 in terms of function of α, β is
- A(α, −β)
- A(−α, −β)
- A(−α, β)
- none of the above
Q. If A and B are non-singular, symmetric and commutable matrices, then A−1B−1 is
- Symmetric matrix
- Identity matrix
- Skew-symmetric matrix
- None of these
Q. Let A, B be square matrix such that A B = 0 and B is non singular then
- |A| must be zero but A may non zero
- A must be zero matrix
- nothing can be said in general about A
- none of these
Q. A square matrix A is said to be nilpotent of index m. If Am=0, now, if for this A , (I−A)n=I+A+A2+...+Am−1, then n is equal to
- \N
- m
- - m
- - 1
Q.
Suppose A is a non-singular matrix such that A3−3A2+6A−I=0. Then, A−1=
A3−3A2+6A
A2−3A+6I
A2+3A−6I
A3+3A2+6A
Q. Let A, B, C be three square matrices of order 3×3 such that A2+2I=0, |(2C−A2)|=30 and satisfying the equation A5−2A3C+BA2−2BC=0
Value of (det.(B−A))2 is
Value of (det.(B−A))2 is
- 8
- -8
- 64
- -64
Q. Let P be a non-singular matrix such that I+P+P2+⋯+Pn=O. Then P−1 is equal to
- P
- −Pn
- Pn−1
- Pn
Q. If A=⎡⎣1tanθ2−tanθ21⎤⎦ and AB = I, then B =
- cos2θ2.A
- cos2θ2.AT
- cos2θ2.I
- None of these
Q. If A is a 3×3 non-singular matrix such that AAT=ATAandB=A−1AT, then BBT is equal to
- I + B
- I
- B−1
- (B−1)T
Q. Let f(α)=⎡⎢⎣cosα−sinα0sinαcosα0001⎤⎥⎦, then (f(α))−1 is equal to
- f(α)
- f(−α)
- f(α−1)
- none
Q. Let A, B, C be three square matrices of order 3×3 such that A2+2I=0, |(2C−A2)|=30 and satisfying the equation A5−2A3C+BA2−2BC=0
Value of (det.(B))2 is
Value of (det.(B))2 is
- 64
- -64
- 512
- -512
Q.
The value of is.
Q. If A and B are square matrices of the same order and A is non-singular, then for a positive integer n, (A−1BA)n is equal to
- A−nBnAn
- AnBnA−n
- A−1BnA
- n(A−1BA)
Q.
Express the following difference in the simplest form
Q. If y=∣∣
∣∣sinxcosxsinxcosx−sinxcosxx11∣∣
∣∣, then the value of dydx=
Q. Matrices P and Q satisfies PQ=Q−1, where Q=(2−120]. Find the value of K for which KP−2Q−1+I=0.
- 2
- 3
- 4
- 6
Q. Inverse of ⎛⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜⎝90000002000000500000080000008800000055⎤⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥⎦ is ⎛⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜⎝1/90000001/20000001/50000001/80000001/880000001/55⎤⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥⎦
- True
- False
Q.
If , find the value of .
Q. If A is square matrix of order n, then |adj(A)| =
- ∣∣A∣∣n−1
- |A|n
- ∣∣A∣∣n−2
- (A|