Mathematics

Equality of matrices

In this Class 12 Mathematics topic from the Matrix chapter, students learn when two matrices are considered equal. They examine the requirement that both matrices have the same order and that every pair of corresponding elements is equal. The topic also shows how matrix equality can be used to compare entries, form equations, and find unknown values. Clear examples help students apply these conditions accurately in algebraic problems.

Easy · Level 1 · 3 questions

Practice questions

01If \(A=\begin{bmatrix}x&2\\3&4\end{bmatrix}\) and \(B=\begin{bmatrix}5&2\\3&4\end{bmatrix}\) and \(A=B\), what is the value of \(x\)?

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Answer and explanation

Correct answer: D. 5

For two equal matrices, their corresponding entries are equal. Here the (1,1) entries are \(x\) and \(5\), so \(x=5\). Option C (4) might mislead since 4 appears in the (2,2) position, but equality demands comparing the same positions, not different ones. Exam tip: always equate entries at the same row and column indices when matrices are equal (compare (i,j) with (i,j)).

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02If \(A=\begin{bmatrix}1&2\\3&4\end{bmatrix}\) and \(B=\begin{bmatrix}1&2\\3&5\end{bmatrix}\), which statement is correct?

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Answer and explanation

Correct answer: B. Matrices are not equal

Two matrices are equal only if they have the same order and every corresponding entry is equal. Both A and B are 2×2 and entries (1,2,3) match, but the (2,2) entries are 4 and 5 which are different. Hence A ≠ B. Option A is wrong because one corresponding entry differs; option C is wrong because both matrices have the same order (2×2); option D is wrong because neither matrix is a zero matrix. Exam tip: to test equality check order first, then compare each corresponding element one by one.

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03If \(A=\begin{bmatrix}x&1\\2&y\end{bmatrix}\) and \(B=\begin{bmatrix}3&1\\2&4\end{bmatrix}\) and \(A=B\), what is \((x,y)\)?

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Answer and explanation

Correct answer: A. \((3,4)\)

Equal matrices have equal corresponding entries. From the (1,1) entry we get \(x=3\), and from the (2,2) entry \(y=4\). Hence \((x,y)=(3,4)\). The closest distractor \((4,3)\) is wrong because it swaps the values of x and y. Exam tip: always equate entries at the same (row,column) positions when comparing matrices.

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Equality of matrices

Practice questions

02If \(A=\begin{bmatrix}1&2\\3&4\end{bmatrix}\) and \(B=\begin{bmatrix}1&2\\3&5\end{bmatrix}\), which statement is correct?यदि \(A=\begin{bmatrix}1&2\\3&4\end{bmatrix}\) और \(B=\begin{bmatrix}1&2\\3&5\end{bmatrix}\), तो कौन-सा कथन सही है?

03If \(A=\begin{bmatrix}x&1\\2&y\end{bmatrix}\) and \(B=\begin{bmatrix}3&1\\2&4\end{bmatrix}\) and \(A=B\), what is \((x,y)\)?यदि \(A=\begin{bmatrix}x&1\\2&y\end{bmatrix}\) और \(B=\begin{bmatrix}3&1\\2&4\end{bmatrix}\) तथा \(A=B\), तो \((x,y)\) क्या है?

Analytics choices

02If \(A=\begin{bmatrix}1&2\\3&4\end{bmatrix}\) and \(B=\begin{bmatrix}1&2\\3&5\end{bmatrix}\), which statement is correct?

03If \(A=\begin{bmatrix}x&1\\2&y\end{bmatrix}\) and \(B=\begin{bmatrix}3&1\\2&4\end{bmatrix}\) and \(A=B\), what is \((x,y)\)?