Advertisements
Advertisements
Question
If A, B are non-singular square matrices of the same order, then (AB–1)–1 = ______.
Options
A–1B
A–1B–1
BA–1
AB
Solution
If A, B are non-singular square matrices of the same order, then (AB–1)–1 = `underline(bb(BA^-1))`.
Explanation:
(AB–1)–1 = (B–1)–1A–1 = BA–1
APPEARS IN
RELATED QUESTIONS
A school wants to award its students for the values of Honesty, Regularity and Hard work with a total cash award of Rs 6,000. Three times the award money for Hard work added to that given for honesty amounts to Rs 11,000. The award money given for Honesty and Hard work together is double the one given for Regularity. Represent the above situation algebraically and find the award money for each value, using matrix method. Apart from these values, namely, Honesty, Regularity and Hard work, suggest one more value which the school must include for awards.
A trust invested some money in two type of bonds. The first bond pays 10% interest and second bond pays 12% interest. The trust received Rs 2,800 as interest. However, if trust had interchanged money in bonds, they would have got Rs 100 less as interest. Using matrix method, find the amount invested by the trust. Interest received on this amount will be given to Helpage India as donation. Which value is reflected in this question?
Find the inverse of each of the matrices, if it exists.` [(2,1),(1,1)]`
Find the inverse of each of the matrices, if it exists.
`[(3,1),(5,2)]`
Find the inverse of each of the matrices, if it exists.
`[(4,5),(3,4)]`
Find the inverse of each of the matrices, if it exists.
[(3,10),(2,7)]
`Find the inverse of each of the matrices, if it exists.
`[(3,-1),(-4,2)]`
Find the inverse of each of the matrices, if it exists.
`[(2, -6),(1, -2)]`
Find the inverse of each of the matrices, if it exists.
`[(6,-3),(-2,1)]`
Find the inverse of each of the matrices, if it exists.
`[(2,-3),(-1,2)]`
Find the inverse of each of the matrices, if it exists.
`[(2,1),(4,2)]`
Find the inverse of each of the matrices, if it exists.
`[(2,-3,3),(2,2,3),(3,-2,2)]`
Find the inverse of each of the matrices, if it exists.
`[(2,0,-1),(5,1,0),(0,1,3)]`
Find the inverse of each of the matrices, if it exists.
`[(1,3,-2),(-3,0,-5),(2,5,0)]`
Find the inverse of each of the matrices, if it exists.
`[(2,0,-1),(5,1,0),(0,1,3)]`
If A is a 3 × 3 invertible matrix, then what will be the value of k if det(A–1) = (det A)k
if `A = ((2,3,1),(1,2,2),(-3,1,-1))`, Find `A^(-1)` and hence solve the system of equations 2x + y – 3z = 13, 3x + 2y + z = 4, x + 2y – z = 8
If |A| = 3 and \[A^{- 1} = \begin{bmatrix}3 & - 1 \\ - \frac{5}{3} & \frac{2}{3}\end{bmatrix}\] , then write the adj A .
If A is 3 × 3 invertible matrix, then show that for any scalar k (non-zero), kA is invertible and `("kA")^-1 = 1/"k" "A"^-1`
Find inverse, by elementary row operations (if possible), of the following matrices
`[(1, 3),(-5, 7)]`
Find inverse, by elementary row operations (if possible), of the following matrices
`[(1, -3),(-2, 6)]`
If A and B are invertible matrices of the same order, then (AB)-1 is equal to ____________.
A matrix in which the number of rows are equal to the number of columns is said to be a
If A and B are invertible square matrices of the same order, then which of the following is not correct?