If A, B, and C are three square matrices of the same order, then `AB=AC implies B=C`. Then

Question

If A, B, and C are three square matrices of the same order, then `AB=AC implies B=C`. Then

If A, B, and C are three square matrices of the same order, then `AB=AC implies B=C`. Then
A. `|A| ne 0`
B. A is invertible
C. A may be orthogonal
D. A is symmetric

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

Related Questions

`nto`Orbit no , `zto` Atomic no `implies r_(n.z)to` Radius `v_(n.z)to` Velocity `T_(n.z)to` Time period of Revolution `implies K_(n.z)to` kinetic ener

2 Answers 5 Views

If A and B are square matrices of the same order, then (i) (AB)=......... (ii) (KA)=.......... (where, k is any scalar) (iii) [k(A-B)]=......

2 Answers 6 Views

If A and B are square matrices of the same order such that `A B=B A` , then show that `(A+B)^2=a^2+2A B+B^2`

2 Answers 5 Views

If `Aa n dB` are square matrices of the same order and `A` is non-singular, then for a positive integer `n ,(A^(-1)B A)^n` is equal to `A^(-n)B^n A^n`

2 Answers 5 Views

Let A and B be two nonsingular square matrices, `A^(T)` and `B^(T)` are the tranpose matrices of A and B, respectively, then which of the following ar

2 Answers 4 Views

Let A and B be square matrices of the same order such that `A^(2)=I` and `B^(2)=I`, then which of the following is CORRECT ?

2 Answers 5 Views

A, B and C are three square matrices of order 3 such that A= diag. (x, y, x), det. `(B)=4` and det. `(C)=2`, where `x, y, z in I^(+)`. If det. (adj. (

2 Answers 4 Views

Let A and B two symmetric matrices of order 3. Statement 1 : `A(BA)` and `(AB)A` are symmetric matrices. Statement 2 : `AB` is symmetric matrix if mat

2 Answers 8 Views

Let `A`, `B` are square matrices of same order satisfying `AB=A` and `BA=B` then `(A^(2010)+B^(2010))^(2011)` equals.

2 Answers 6 Views

If `A`, `B` are two square matrices of same order such that `A+B=AB` and `I` is identity matrix of order same as that of `A`,`B` , then

2 Answers 5 Views

Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

If `|A| ne 0`, then
`AB=AC`
or `A^(-1) AB=A^(-1) AC`
or `B=C`
Also, if A is orthogonal matrix, then `A A^(T)=I`
`implies |A A^(T)|=1 implies |A|^(2)=1implies` is invertible

4 views Answered 2023-02-05 15:29