Test Index

AP DSC School Assistant Math Model Test 2

Section: Subject Specific

Question : 99 of 160

Marks: +1, -0

B = C provided

Solution:

Concept:

If a matrix is non-singular (determinant non-zero), its inverse exists, allowing cancellation in matrix equations.

Explanation:

Given

AB = AC

. If

|A| \neq 0

, then

A

is invertible, and

A^{-1}

exists. Multiply both sides on the left by

A^{-1}

A^{-1}(AB) = A^{-1}(AC)

Using associativity:

(A^{-1}A)B = (A^{-1}A)C

Since

A^{-1}A = I

, we get

IB = IC

, i.e.,

B = C

Thus,

B = C

holds when

A

is non-singular.

Answer:

Option B:

|A| \neq 0

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