If A = 0 2 3 – 4 and kA = 0 3 a 2 b 24 then find the value of b – a- k.
If A = 1 − 2 3 , B = 2 − 3 − 1 , then AB is equal to
Let A = 3 2 1 1 satisfies A 2 + a A + b I = O , then a, b are respectively equal to
The values of λ for which the matrix A = λ 0 λ λ 0 − λ 0 1 0 is orthogonal is
If A = − 4 − 1 3 1 then the determinant line matrix A 2016 − 2 A 2015 − A 2014 , is
If AB = A and BA = B, where A c. · B are square matrices, then
If the matrix A = 1 2 3 0 2 4 3 2 3 2 1 3 6 8 7 α is of rank 3 Then α =
The rank of 1 4 − 1 2 3 0 0 1 2 is
If 2 α + 1 3 β 0 β 2 − 5 β = α + 3 β 2 + 2 0 − 6 find the value of α + β
If A = 1 2 2 3 and A 2 – λA – I 2 = O , then λ is equal to
Let A, B be two 3 × 3 matrices with entries from real numbers. Which one of the following is true?
If A is a skew Hermitian matrix, then the main diagonal elements of A are all
If A = cos θ sin θ − sin θ cos θ , then A 2 = 1 is true for
A value of b for which the rank of the matrix is A = 1 1 – 1 0 4 4 – 3 1 b 2 2 2 9 9 b 3 is 3, is
Let A , B be two n × n matrices such that A + B = A B , then
If A, B are two square matrices such that AB =A and BA = B, then
If the trace of A is 20 and the trace of B is 5 then find the trace of (A -B).
If A = i − i − i i and B = 1 − 1 − 1 1 , then A 8 equals
If A is an orthogonal matrix, then | A | is
If A is a square matrix then which one of the following is not a symmetric matrix
If A = 1 2 3 4 , then A 2 − 5 A − I equals
A = 1 2 3 1 2 3 − 1 − 2 − 3 , then A is a nilpotent matrix of index
If A = a b b a and A 2 = α β β α , then
The matrix A = p − q q p is orthogonal if and only if
If A α = cos α sin α − sin α cos α , then A α A β is equal to
If A and B two are 3×3 matrices, then which one of following is not true:
If A and B are two skew-symmetric matrices of order n, then
The number of values of λ for which there exist a non-zero 3×3 matrix A such that A ′ = λ A is :
If A and B are symmetric matrices, then AB – BA is a
Suppose A is a 3×3 skew-symmetric matrix. Let B = ( I + A ) − 1 ( I − A ) . Then
If A = a b b 2 − a 2 − a b , then A 2 is equal
If A is 2 × 2 matrix such that A 2 = O , then t r ( A ) is
Let A = a â â â â b c â â â â d be such that A 3 = O but A â O , then
If A = 1 0 0 0 1 0 a b – 1 then A 2 is equal to
If A = 1 − 1 2 − 1 , B = a 1 b − 1 and ( A + B ) 2 = A 2 + B 2 then the values of a and b are
{f A and B are two matrices such that A B = A and A = B , then B 2 is equal to
if A and B are two matrices such that AB = B and BA = A, then A 2 + B 2 is equal to
If the rank of x x x x x 2 x x x x + 1 is 1, then
Solve for x and y , x 2 1 + y 3 5 + − 8 − 11 = 0
Total number of possible matrices of order 3×3 with each entry 2 or 0 is
If A is a square matrix such that A 2 = I , then (A-I) 3 +(A+I) 3 -7A is equal to
Let A = 2 3 − 1 2 and f ( x ) = x 2 − 4 x + 7 Show that f ( A ) = O Use this result to find A 5
If A α = cos α sin α − sin α cos α then that A α . A β =
if w is a complex cube root of unity, than 1 w w 2 w w 2 1 w 2 1 w + w w 2 1 w 2 1 w w w 1 1 w w 2 =
If 1 1 0 1 1 2 0 1 1 3 0 1 ⋯ ⋯ · 1 n – 1 0 1 = 1 78 0 1 then the inverse of 1 n 0 1 is
The rank of 1 4 − 1 2 3 0 0 1 2 is
If A = 0 1 0 0 0 1 − c − b − a then A 3 + a A 2 + b A + c I is
If D = diag d 1 , d 2 , d 3 , … , d n , where d i ≠ 0 for all i =1,2,.. n, then D -1 is equal to
If A = ab b 2 − a 2 − ab then A is
In a 2 x 3 matrix A = a ij whose elements are given a ij = 1 2 | 2 i − 3 j | t h e n a 11 =
If x + 3 2 y + x z − 1 4 w − 8 = − x − 1 0 3 2 w then find the value of | x + y | + | z + w |
Determine the matrix A When A = 4 1 2 3 – 1 – 2 – 3 4 2 6 + 2 5 4 1 3 2 4 3 8 2
Find the sum of all elements in X where 2 X − Y = 3 − 3 0 3 3 2 , 2 Y + X = 4 1 5 − 1 4 − 4
If A = 1 – 1 2 – 1 , B = a 1 b – 1 and A + B 2 = A 2 + B 2 , the value of a + b is
If A = 0 α 0 0 and A + I 50 – 50 A = a b c d , the value of a + b + c + d is
If A = 1 2 x 0 1 0 0 0 1 and B = 1 – 2 y 0 1 0 0 0 1 and AB = I 3 , then x + y equal to
A and B be 3 x 3 matrices. Then, AB = O implies
If A = 1 – 5 7 0 7 9 11 8 9 ,then trace of matrix A, is
If A = a ij 4 × 4 such that a ij = ( i + j ) 2 then find trace of A.
If A = a ij 3 × 3 and a ij = i ( i + j ) then trace of A.
If the trace of a matrix A is 3 then find the trace of 5A.
If the trace of AB is 25 then find the trace of BA.
If A = a ij is a scalar matrix of order n x n such that a ij = k for all i=j, then trace of A is
If A = x − y y − z z − x y − z z − x x − y z − x x − y y − z ,then trace of A is
If the traces of A, B are 20 and -8 then find the trace of (A + B).
If A = cos θ − sin θ sin θ cos θ ,then A T + A = I 2 if
If A and B are symmetric matrices, then AB- BA is a
If A = i 0 0 i , n ∈ N , then A 4n equals
If AB = A and BA = B, then B 2 is equal to
If X = 3 – 4 1 – 1 , the value of X n is
If A and B are two matrices such that AB = B and BA = A, then A 2 + B 2 =
If A and B are square matrices of same order such that (A + B) 2 = A 2 + B 2 + 2AB, then
If A = A = i – i – i i a n d B = 1 – 1 – 1 1 the A 8 equals
If A and B are two matrices such that A + B and AB are both defined, then
If A = 1 0 1 / 2 1 , then A 100 is equal to
If A is 3 × 4 matrix and B is a matrix such that A′B and BA′ are both defined. Then B is of the type
If P = 3 2 1 2 – 1 2 3 2 , A = 1 1 0 1 a n d Q = P A P T , t h e n P T ( Q 2005 ) P is equal to
If A is symmetric as well as skew symmetric matrix, then A is
If A is a 3 × 3 skew-symmetric matrix, then trace of A is
If A is an orthogonal matrix, then |A| is
Let A = 0 2 b c a b – c a – b c be an orthogonal matrix then the values of a, b, c are
Which of the following is correct?
If 1 4 2 0 = x y 2 z 0 , y < 0 then x − y + k is equal to
If A = − i 0 0 i , then A’ A is equal to
If A − 2 B = 1 5 3 7 and 2 A − 3 B = − 2 5 0 7 , then matrix B is equal to
If A = cos θ − sin θ sin θ cos θ , then
If A = 2 3 − i − i 3 + i π 7 + i i 7 − i e , then A is
If I = 1 0 0 1 , J = 0 1 − 1 0 and B = cos θ sin θ − sin θ cos θ then B equals
If A is both diagonal and skew-symmetric, then
If A = a i j 3 × 3 where a i j = cos ( i + j ) then
If i 0 3 − i + X = i 2 3 4 + i − X then X is equal to
If A = 0 − i i 0 , B = 1 0 0 − 1 ,then A B + B A is
If A is a 2 × 2 unitary matrix, then |A| is equal to
If A is a 3 x 3 skew-symmetric matrix with real entries and trace of A 2 equals zero, then
If A 2 = A , the ( I + A ) 4 equals
The values of a for which the matrix A = a a 2 − 1 − 3 a + 1 2 a 2 + 4 − 3 4 a − 1 is symmetric are
If A = 0 2 y z x y − z x − y z satisfies A ′ = A − 1 , then
The values of a for which the matrix A = a a 2 − 1 − 3 a + 1 2 a 2 + 4 − 3 4 a − 1 is symmetric are
If A is 2 × 2 matrix such that A 2 = O, then t r ( A ) is
If A = 1 2 1 0 1 â 1 3 â 1 1 then A 3 â 3 A 2 â A + 9 I is equal to
Let A = 4 3 2 5 and x , y ∈ R are such that A 2 + x A + y I = 0 then (x,y) equals
If A and B are two square matrices of the same order, then which of the following is true.
Let A = 1 â â â â 2 3 â â â â 4 and B = a â â â â 0 0 â â â â b , a , b â N
If A = cos ⡠α â sin ⡠α sin ⡠α cos ⡠α and A + A â² = I , then α equals
If A and B are two matrices such that AB =B and BA = A, then A 2 + B 2 is equal to
If A = 2 0 1 2 1 3 1 − 1 0 , then A 2 − 5 A + 6 I is equal to
.If A B = A and B A = B , where A c . · B are square matrices, then
If A and B are two matrices such that AB = A and BA = B, then B 2 is equal to
If A = i 0 0 i , n ∈ N , then A 4 n equals
if A and B are two matrices such that A B = B and B A = A , then A 2 + B 2 is equal to
If the matrix AB is zero, then
The matrix A = 1 − 3 − 4 − 1 3 4 1 − 3 − 4 is nilpotent index
